This paper proposes a new Zernike modal gray map reconstruction algorithm used in the nematic liquid crystal adaptive optics system. Firstly, the new modal algorithm is described. Secondly, a single loop correction ex...This paper proposes a new Zernike modal gray map reconstruction algorithm used in the nematic liquid crystal adaptive optics system. Firstly, the new modal algorithm is described. Secondly, a single loop correction experiment was conducted, and it showed that the modal method has a higher precision in gray map reconstruction than the widely used slope method. Finally, the contrast close-loop correction experiment was conducted to correct static aberration in the laboratory. The experimental results showed that the average peak to valley (PV) and root mean square (RMS) of the wavefront corrected by mode method were reduced from 2.501A (λ= 633 nm) and 0.610A to 0.0334λ and 0.00845A, respectively. The corrected PV and RMS were much smaller than those of 0.173A and 0.048A by slope method. The Strehl ratio and modulation transfer function of the system corrected by mode method were much closer to diffraction limit than with slope method. These results indicate that the mode method can take good advantage of the large number of pixels of the liquid crystal corrector to realize high correction precision.展开更多
A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the followi...A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed.Constructing large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed.This paper presents a new effective and easy technique,adjusted Gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation functions.Theoretical justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level designs.The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.展开更多
In this paper, we study λ-constacyclic codes over the ring R = Z4 + uZ4, where u^2 = 0, for λ= 1 + 3u and 3 + u. We introduce two new Gray maps from R to Z4^4 and show that the Gray images of λ-constacyclic cod...In this paper, we study λ-constacyclic codes over the ring R = Z4 + uZ4, where u^2 = 0, for λ= 1 + 3u and 3 + u. We introduce two new Gray maps from R to Z4^4 and show that the Gray images of λ-constacyclic codes over R are quasi-cyclic over Z4. Moreover, we present many examples of λ-constacyclic codes over R whose Z4-images have better parameters than the currently best-known linear codes over Z4.展开更多
Gray mapping is a well-known way to improve the performance of regular constellation modulation,but it is challenging to be applied directly for irregular alternative.To address this issue,in this paper,a unified bit-...Gray mapping is a well-known way to improve the performance of regular constellation modulation,but it is challenging to be applied directly for irregular alternative.To address this issue,in this paper,a unified bit-to-symbol mapping method is designed for generalized constellation modulation(i.e.,regular and irregular shaping).The objective of the proposed approach is to minimize the average bit error probability by reducing the hamming distance(HD)of symbols with larger values of pairwise error probability.Simulation results show that the conventional constellation modulation(i.e.,phase shift keying and quadrature amplitude modulation(QAM)with the proposed mapping rule yield the same performance as that of classical gray mapping.Moreover,the recently developed golden angle modulation(GAM)with the proposed mapping method is capable of providing around1 d B gain over the conventional mapping counterpart and offers comparable performance to QAM with Gray mapping.展开更多
Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to...Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to is defined which preserves self duality of linear codes. As a consequence self-dual, formally self-dual and self-orthogonal codes over are constructed. Some examples are also given to illustrate this.展开更多
Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/<u^(2)=1,v^(2)=0,uv=vu=0>for a unit Λ=1+2u+2v in R.We define several Gray map...Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/<u^(2)=1,v^(2)=0,uv=vu=0>for a unit Λ=1+2u+2v in R.We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over Z_(4) are cyclic,quasi-cyclic or permutation equivalent to this code.For an odd positive integer n,we determine the generator polynomials of cyclic and Λ-constacyclic codes of length n over R.Further,we prove that a(θ,Λ)-cyclic code of length n is a Λ-constacyclic code if n is odd,and a Λ-quasi-twisted code if n is even.A few examples are also incorporated,in which two parameters are new and one is best known to date.展开更多
By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and suffi...By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular,(1 +(v +1)ap)-constacyclic codes over R are classified in terms of generator polynomial, where a is a unit of Z m.展开更多
We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cycli...We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2.展开更多
In this work, we investigate the cyclic codes over the ring F2+ uF2+ vF2. We first study the relationship between linear codes over F2+ uF2+ vF2 and that over F2.Then we give a characterization of the cyclic codes ove...In this work, we investigate the cyclic codes over the ring F2+ uF2+ vF2. We first study the relationship between linear codes over F2+ uF2+ vF2 and that over F2.Then we give a characterization of the cyclic codes over F2+ uF2+ vF2. Finally, we obtain the number of the cyclic code over F2+ uF2+ vF2 of length n.展开更多
The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the...The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the nonlinear code constructed by Goethals in 1976.展开更多
Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub&g...Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.展开更多
This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^...This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^(k_2)8^(k_3)4^(k_4)4^(k_5)4^(k_6)2^(k_7)2^(k_8) based on a distance-preserving Gray map from(Z4 + u Z4)n to Z2n4. Secondly, the authors use the similar approach to do works on two-Gray(projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.展开更多
Abstract Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over Fp + uFp ...Abstract Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over Fp + uFp + u^2Fp and codes over Fp is defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear (1 + u + u2)-constacyclic code over Fp + uFp + u^2Fp of length n is a repeated-root cyclic code over Fp of length pn. Furthermore, some examples of optimal linear cyclic codes over F3 from (1 + u + u2)-constacyclic codes over F3 + uF3 + u^2F3 are given.展开更多
This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z4.The authors first give the Pless identities on the Lee weight of linear codes over Z_4.Then the...This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z4.The authors first give the Pless identities on the Lee weight of linear codes over Z_4.Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively,the construction methods of one-Lee weight and two-Lee weight projective codes over Z4 are also given.Finally,the authors recall the weight-preserving Gray map from(Z_4~n,Lee weight)to(F_2^(2n),Hamming weight),and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes,which reach the Plotkin bound and the Griesmer bound.展开更多
This paper studies (1 + u)-constacyelic codes over the ring F2 + uF2 + vF,2 + uvF2. It is proved that the image of a (1 + u)-constacyclic code of length n over F2 + uF2 + vF2 +uvF2 under a Gray map is a di...This paper studies (1 + u)-constacyelic codes over the ring F2 + uF2 + vF,2 + uvF2. It is proved that the image of a (1 + u)-constacyclic code of length n over F2 + uF2 + vF2 +uvF2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined, Some optimal binary codes are obtained directly from (1 + u)-constacyclic codes over F2 + uF2 + vF2 + uvF2.展开更多
This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preservi...This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preserving Gray map from( IFp + v IFp)nto2np. By the Gray map, the authors construct a family of optimal one-Hamming weight p-ary linear codes from one-Lee weight codes over IFp+ v IFp, which attain the Plotkin bound and the Griesmer bound. The authors also obtain a class of optimal p-ary linear codes from two-Lee weight projective codes over IFp + vIFp, which meet the Griesmer bound.展开更多
Constacyclic codes are an important class of linear codes in coding theory.Many optimal linear codes are directly derived from constacyclic codes.In this paper,(1 — uv)-constacyclic codes over the local ring F_p + uF...Constacyclic codes are an important class of linear codes in coding theory.Many optimal linear codes are directly derived from constacyclic codes.In this paper,(1 — uv)-constacyclic codes over the local ring F_p + uF_p + vF_p + uvF_p are studied.It is proved that the image of a(1 — uv)-constacyclic code of length n over F_p + uF_p + vF_p + uvF_p under a Gray map is a distance invariant quasi-cyclic code of index p2 and length p^3n over F_p.Several examples of optimal linear codes over F_p from(1 — uv)-constacyclic codes over F_p + uF_p + vF_p + uvF_p are given.展开更多
This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~...This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~n, Lee weight) to(IF_p^(2 n), Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p=2.展开更多
The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the ...The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.展开更多
Orthogonal frequency division multiplexing (OFDM) is sensitive to carrier frequency offset (CFO), which destroys the orthogonality and causes inter-carrier interference (ICI). ICI self-cancellation schemes based...Orthogonal frequency division multiplexing (OFDM) is sensitive to carrier frequency offset (CFO), which destroys the orthogonality and causes inter-carrier interference (ICI). ICI self-cancellation schemes based on polynomial cancellation coding (PCC-OFDM) can evidently reduce the sensitivity to CFO. In this paper, we analyze the performance of PCC-OFDM systems impaired by CFO over additive white gaussian noise (AWGN) channels. Two criteria are used to evaluate the effect of CFO on performance degradations. Firstly, the closed-form expressions of the average carrier-to-interference power ratio (CIR) and the statistical average ICI power, both of which reflect the desired power loss, are presented. Simulation and analytical results show that the theoretical expressions depend crucially on the normalized frequency offset and are hardly relevant to the number of subcarriers. Secondly, by exploiting the properties of the Beaulieu series, the effect of CFO on symbol error rate (SER) and bit error rate (BER) performance for PCC-OFDM systems are exactly expressed as the sum of an infinite series in terms of the charac- teristic function (CHF) of ICI. We consider the systems modulated with binary phase shift keying (BPSK), quadrature PSK (QPSK), 8-ary PSK (8-PSK), and 16-ary quadrature amplitude modulation (16-QAM), and all above modulation schemes are mapped with Gray codes for the evaluations of BER.展开更多
基金Project supported by the National Natural Science Foundation of China (Grants Nos.60736042,60578035 and 50703039)Science and Technology Cooperation Project between Chinese Academy of Sciences and Jilin Province (Grant No.2008SYHZ0005)
文摘This paper proposes a new Zernike modal gray map reconstruction algorithm used in the nematic liquid crystal adaptive optics system. Firstly, the new modal algorithm is described. Secondly, a single loop correction experiment was conducted, and it showed that the modal method has a higher precision in gray map reconstruction than the widely used slope method. Finally, the contrast close-loop correction experiment was conducted to correct static aberration in the laboratory. The experimental results showed that the average peak to valley (PV) and root mean square (RMS) of the wavefront corrected by mode method were reduced from 2.501A (λ= 633 nm) and 0.610A to 0.0334λ and 0.00845A, respectively. The corrected PV and RMS were much smaller than those of 0.173A and 0.048A by slope method. The Strehl ratio and modulation transfer function of the system corrected by mode method were much closer to diffraction limit than with slope method. These results indicate that the mode method can take good advantage of the large number of pixels of the liquid crystal corrector to realize high correction precision.
基金supported by the UIC Research Grants with No.of(R201912 and R202010)the Curriculum Development and Teaching Enhancement with No.of(UICR0400046-21CTL)+1 种基金the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU-HKBU United International College with No.of(2022B1212010006)Guangdong Higher Education Upgrading Plan(2021-2025)with No.of(UICR0400001-22).
文摘A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed.Constructing large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed.This paper presents a new effective and easy technique,adjusted Gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation functions.Theoretical justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level designs.The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.
文摘In this paper, we study λ-constacyclic codes over the ring R = Z4 + uZ4, where u^2 = 0, for λ= 1 + 3u and 3 + u. We introduce two new Gray maps from R to Z4^4 and show that the Gray images of λ-constacyclic codes over R are quasi-cyclic over Z4. Moreover, we present many examples of λ-constacyclic codes over R whose Z4-images have better parameters than the currently best-known linear codes over Z4.
基金supported in part by the National Key Research and Development Program of China under Grant 2021YFB2900502in part by the National Science Foundation of China under Grant 62001179in part by the Fundamental Research Funds for the Central Universities under Grant 2020kfy XJJS111。
文摘Gray mapping is a well-known way to improve the performance of regular constellation modulation,but it is challenging to be applied directly for irregular alternative.To address this issue,in this paper,a unified bit-to-symbol mapping method is designed for generalized constellation modulation(i.e.,regular and irregular shaping).The objective of the proposed approach is to minimize the average bit error probability by reducing the hamming distance(HD)of symbols with larger values of pairwise error probability.Simulation results show that the conventional constellation modulation(i.e.,phase shift keying and quadrature amplitude modulation(QAM)with the proposed mapping rule yield the same performance as that of classical gray mapping.Moreover,the recently developed golden angle modulation(GAM)with the proposed mapping method is capable of providing around1 d B gain over the conventional mapping counterpart and offers comparable performance to QAM with Gray mapping.
文摘Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to is defined which preserves self duality of linear codes. As a consequence self-dual, formally self-dual and self-orthogonal codes over are constructed. Some examples are also given to illustrate this.
文摘Let Z_(4) be the ring of integers modulo 4.We study the Λ-constacyclic and(θ,Λ)-cyclic codes over the non-chain ring R=Z_(4)[u,v]/<u^(2)=1,v^(2)=0,uv=vu=0>for a unit Λ=1+2u+2v in R.We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over Z_(4) are cyclic,quasi-cyclic or permutation equivalent to this code.For an odd positive integer n,we determine the generator polynomials of cyclic and Λ-constacyclic codes of length n over R.Further,we prove that a(θ,Λ)-cyclic code of length n is a Λ-constacyclic code if n is odd,and a Λ-quasi-twisted code if n is even.A few examples are also incorporated,in which two parameters are new and one is best known to date.
基金Supported by the National Natural Science Foundation of China(No.61370089)
文摘By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular,(1 +(v +1)ap)-constacyclic codes over R are classified in terms of generator polynomial, where a is a unit of Z m.
基金Foundation item: Supported by the Scientific Research Foundation of Education Department of Hubei Province(B2013069) Supported by the National Science Foundation of Hubei Polytechnic University of China (12xjzl4A, llyjz37B)
文摘We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2.
基金Foundation item: Supported by the Scientific Research Foundation of Education Department of Hubei Province(B2013069) Supported by the National Science Foundation of Hubei Polytechnic University of China(12xjz14A,11yjz37B)
文摘In this work, we investigate the cyclic codes over the ring F2+ uF2+ vF2. We first study the relationship between linear codes over F2+ uF2+ vF2 and that over F2.Then we give a characterization of the cyclic codes over F2+ uF2+ vF2. Finally, we obtain the number of the cyclic code over F2+ uF2+ vF2 of length n.
文摘The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the nonlinear code constructed by Goethals in 1976.
文摘Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.
基金supported by the National Natural Science Foundation of China under Grant Nos.61672036 and 61202068the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2015D11+1 种基金Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China under Grant No.05015133Key projects of support program for outstanding young talents in Colleges and Universities under Grant No.gxyq ZD2016008
文摘This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^(k_2)8^(k_3)4^(k_4)4^(k_5)4^(k_6)2^(k_7)2^(k_8) based on a distance-preserving Gray map from(Z4 + u Z4)n to Z2n4. Secondly, the authors use the similar approach to do works on two-Gray(projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.
基金supported by the National Natural Science Foundation of China under Grant No.61370089the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2014D04+3 种基金the Natural Science Fund of Education Department of Anhui province under Grant No.KJ2013Z276the Fundamental Research Funds of Hefei University under Grant No.10KY01ZDthe Key construction discipline Funds of Hefei University under Grant No.2014XK08the Natural Science Key Fund of Education Department of Anhui Province under Grant No.KJ2015A226
文摘Abstract Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over Fp + uFp + u^2Fp and codes over Fp is defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear (1 + u + u2)-constacyclic code over Fp + uFp + u^2Fp of length n is a repeated-root cyclic code over Fp of length pn. Furthermore, some examples of optimal linear cyclic codes over F3 from (1 + u + u2)-constacyclic codes over F3 + uF3 + u^2F3 are given.
基金supported by the National Natural Science Foundation of China under Grant Nos.61202068 and 11126174Talents youth Fund of Anhui Province Universities under Grant No.2012SQRL020ZDsupported by Key Discipline Construction of Hefei University 2014XK08
文摘This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z4.The authors first give the Pless identities on the Lee weight of linear codes over Z_4.Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively,the construction methods of one-Lee weight and two-Lee weight projective codes over Z4 are also given.Finally,the authors recall the weight-preserving Gray map from(Z_4~n,Lee weight)to(F_2^(2n),Hamming weight),and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes,which reach the Plotkin bound and the Griesmer bound.
基金supported by the National Natural Science Foundation of China under Grant No.60973125the Natural Science Foundation of Anhui Province under Grant No.1208085MA14the Fundamental Research Funds for the Central Universities under Grants Nos.2012HGXJ0040 and 2011HGBZ1298
文摘This paper studies (1 + u)-constacyelic codes over the ring F2 + uF2 + vF,2 + uvF2. It is proved that the image of a (1 + u)-constacyclic code of length n over F2 + uF2 + vF2 +uvF2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined, Some optimal binary codes are obtained directly from (1 + u)-constacyclic codes over F2 + uF2 + vF2 + uvF2.
基金supported by the National Natural Science Foundation of China under Grant No.61202068Talented youth Fund of Anhui Province Universities under Grant No.2012SQRL020ZDthe Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China under Grant No.05015133
文摘This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preserving Gray map from( IFp + v IFp)nto2np. By the Gray map, the authors construct a family of optimal one-Hamming weight p-ary linear codes from one-Lee weight codes over IFp+ v IFp, which attain the Plotkin bound and the Griesmer bound. The authors also obtain a class of optimal p-ary linear codes from two-Lee weight projective codes over IFp + vIFp, which meet the Griesmer bound.
基金supported by the National Natural Science Foundation of China under Grant No.61370089the Natural Science Foundation of Anhui Province under Grant No.1208085MA14+2 种基金the Natural Science Fund of Education Department of Anhui province under Grant No.KJ2013Z276the Fundamental Research Fundsof Hefei University under Grant No.10KY01ZDthe Key construction discipline Funds of Hefei University under Grant No.2014XK08
文摘Constacyclic codes are an important class of linear codes in coding theory.Many optimal linear codes are directly derived from constacyclic codes.In this paper,(1 — uv)-constacyclic codes over the local ring F_p + uF_p + vF_p + uvF_p are studied.It is proved that the image of a(1 — uv)-constacyclic code of length n over F_p + uF_p + vF_p + uvF_p under a Gray map is a distance invariant quasi-cyclic code of index p2 and length p^3n over F_p.Several examples of optimal linear codes over F_p from(1 — uv)-constacyclic codes over F_p + uF_p + vF_p + uvF_p are given.
基金supported by the National Natural Science Foundation of China under Grant No.61202068Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China under Grant No.05015133+1 种基金the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2015D11Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities under Grant No.gxyqZD2016008
文摘This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~n, Lee weight) to(IF_p^(2 n), Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p=2.
基金supported by the National Natural Science Foundation of China(60773002,60672119 and 60873144)the Program for New Century Excellent Talents in University,the Scientific Research Foundation for the Returned Overseas Chinese Scholars,the Hi-Tech Research and Development Program of China(2007AA01Z472)
文摘The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.
基金Supported by the National Natural Science Foundation of China (Grant No. 60496310)the National High Technology Research and Devel-opment of China, China "863" Plan (Grant No. 2006AA01Z263)The paper is presented in part in Proceedings of IEEE Global Telecommunications Conference 2006 (GLOBECOM’06) in San Francisco, USA, Nov. 2006
文摘Orthogonal frequency division multiplexing (OFDM) is sensitive to carrier frequency offset (CFO), which destroys the orthogonality and causes inter-carrier interference (ICI). ICI self-cancellation schemes based on polynomial cancellation coding (PCC-OFDM) can evidently reduce the sensitivity to CFO. In this paper, we analyze the performance of PCC-OFDM systems impaired by CFO over additive white gaussian noise (AWGN) channels. Two criteria are used to evaluate the effect of CFO on performance degradations. Firstly, the closed-form expressions of the average carrier-to-interference power ratio (CIR) and the statistical average ICI power, both of which reflect the desired power loss, are presented. Simulation and analytical results show that the theoretical expressions depend crucially on the normalized frequency offset and are hardly relevant to the number of subcarriers. Secondly, by exploiting the properties of the Beaulieu series, the effect of CFO on symbol error rate (SER) and bit error rate (BER) performance for PCC-OFDM systems are exactly expressed as the sum of an infinite series in terms of the charac- teristic function (CHF) of ICI. We consider the systems modulated with binary phase shift keying (BPSK), quadrature PSK (QPSK), 8-ary PSK (8-PSK), and 16-ary quadrature amplitude modulation (16-QAM), and all above modulation schemes are mapped with Gray codes for the evaluations of BER.