IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub&g...IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub>i</sub>p<sup>i</sup>（1-p）<sup>n-1</sup>, （1）where （A<sub>0</sub>, A<sub>1</sub>,…, A<sub>n</sub>） is the weight distribution of C. If for all 0≤p≤0.5, P<sub>e</sub>（p）≤P<sub>e</sub>（0. 5） = 2<sup>k-n</sup>-2<sup>-n</sup>, then C is called good for error detection. Moreover, if P<sub>e</sub> （p） ismonotonously increasing in the interval [0, 0.5], then C is called proper. Clearly, propercodes are good.展开更多
Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, ...Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.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
In this paper, the period distribution of cyclic codes overR = F_q + uF_q +···+u^(m-1)F_q is studied, where um= 0 and q is a prime power. A necessary and sufficient condition for the existence of period...In this paper, the period distribution of cyclic codes overR = F_q + uF_q +···+u^(m-1)F_q is studied, where um= 0 and q is a prime power. A necessary and sufficient condition for the existence of period of cyclic codes over R is given. The period distributions of cyclic codes over R and their dual codes are determined by employing generator polynomial. The counting formulas of the period distributions of cyclic codes over R and their dual codes are obtained.展开更多
In this paper, we study skew cyclic codes over the ring Fp +vFp,where p is a odd prime and v 2=1. We give the generators of skew cyclic codes, with the consideration of the dual of skew cyclic codes.
A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several conseq...A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.展开更多
We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or ...We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.展开更多
Though the emerging live streaming industry has attracted growing attention,the dominant yanzhi category where streamers mostly interact with the audience through amateur talent shows and casual chats has not been wid...Though the emerging live streaming industry has attracted growing attention,the dominant yanzhi category where streamers mostly interact with the audience through amateur talent shows and casual chats has not been widely investigated.To decode the mechanism behind the popularity of yanzhi streamers,this study draws on Dual Coding Theory(DCT)to posit that age estimated from a streamer’s face and voice can influence the level of viewer engagement.To validate our hypothesized relationships,274 one-minute video records ahead of a viewer commenting or/and gifting were collected and analyzed via deep learning algorithms.Analytical results attest to the negative effects of both facial and vocal age on viewer engagement,while their interaction has a positive impact on viewer engagement.展开更多
For any odd prime p, a classification of all cyclic and negacyclic codes of length 8ps over Fpm are obtained, which establishes the algebra structures in term of specified polynomial generators of such codes. Among ot...For any odd prime p, a classification of all cyclic and negacyclic codes of length 8ps over Fpm are obtained, which establishes the algebra structures in term of specified polynomial generators of such codes. Among other results, all self-dual negacyclic codes of length 8ps are obtained, and the structures of α-constacyclic and β-constacyclic codes of length 8ps over Fpm are established.展开更多
文摘IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub>i</sub>p<sup>i</sup>（1-p）<sup>n-1</sup>, （1）where （A<sub>0</sub>, A<sub>1</sub>,…, A<sub>n</sub>） is the weight distribution of C. If for all 0≤p≤0.5, P<sub>e</sub>（p）≤P<sub>e</sub>（0. 5） = 2<sup>k-n</sup>-2<sup>-n</sup>, then C is called good for error detection. Moreover, if P<sub>e</sub> （p） ismonotonously increasing in the interval [0, 0.5], then C is called proper. Clearly, propercodes are good.
文摘Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.
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Supported by the National Natural Science Foundation of China(No.61370089)Fundamental Research Funds for the Central Universities(Nos.2013HGCH0024,J2014HGXJ0073)Specialized Research Fund for the Doctoral Program of Hefei University of Technology(No.JZ2014HGBZ0029)
文摘In this paper, the period distribution of cyclic codes overR = F_q + uF_q +···+u^(m-1)F_q is studied, where um= 0 and q is a prime power. A necessary and sufficient condition for the existence of period of cyclic codes over R is given. The period distributions of cyclic codes over R and their dual codes are determined by employing generator polynomial. The counting formulas of the period distributions of cyclic codes over R and their dual codes are obtained.
基金Supported by the National Natural Science Foundation of China(No.61370089)
文摘In this paper, we study skew cyclic codes over the ring Fp +vFp,where p is a odd prime and v 2=1. We give the generators of skew cyclic codes, with the consideration of the dual of skew cyclic codes.
基金The work was supported in part by Harbin Normal University's Natural Scientific fund items (KM2006-20 and KM2005-14)Educational department scientific Technology item (1151112)Postdoctorate's fund item (LRB-KY01043)Scientific Technology Brainstorm item in Hei Longjiang province
文摘A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.
基金This work was supported by the Ministry of Education and Training of Vietnam(Thai Nguyen University)under Grant No.B2019-TNA-02.
文摘We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.
文摘Though the emerging live streaming industry has attracted growing attention,the dominant yanzhi category where streamers mostly interact with the audience through amateur talent shows and casual chats has not been widely investigated.To decode the mechanism behind the popularity of yanzhi streamers,this study draws on Dual Coding Theory(DCT)to posit that age estimated from a streamer’s face and voice can influence the level of viewer engagement.To validate our hypothesized relationships,274 one-minute video records ahead of a viewer commenting or/and gifting were collected and analyzed via deep learning algorithms.Analytical results attest to the negative effects of both facial and vocal age on viewer engagement,while their interaction has a positive impact on viewer engagement.
基金Supported by the Natural Science Foundation of Hubei Province(D20144401)the Natural Science Foundation of Hubei Polytechnic University(12xjz14A)
文摘For any odd prime p, a classification of all cyclic and negacyclic codes of length 8ps over Fpm are obtained, which establishes the algebra structures in term of specified polynomial generators of such codes. Among other results, all self-dual negacyclic codes of length 8ps are obtained, and the structures of α-constacyclic and β-constacyclic codes of length 8ps over Fpm are established.
