This paper proves that if qn is large enough, for each element a and primitive element b of Fq, there etists a primitive polynomial of degree n ≥5 over the finite field Fq having a as the coefficient of xn-1 and b as...This paper proves that if qn is large enough, for each element a and primitive element b of Fq, there etists a primitive polynomial of degree n ≥5 over the finite field Fq having a as the coefficient of xn-1 and b as the constant term. This proves that if qn is large enongh, for each element a ∈Fq, there exists a primitive polynomial of degree n ≥ 5 over Fq having a as the coefficient of x.展开更多
Space-Time Block Coded(STBC)Orthogonal Frequency Division Multiplexing(OFDM)satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel.However,conventional STBCs,including O...Space-Time Block Coded(STBC)Orthogonal Frequency Division Multiplexing(OFDM)satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel.However,conventional STBCs,including Orthogonal STBCs(OSTBCs),Non-Orthogonal(NOSTBCs),and Quasi-Orthogonal STBCs(QOSTBCs),do not provide both maximal diversity order and unity code rate simultaneously for more than two transmit antennas.This paper targets this problem and applies Maximum Rank Distance(MRD)codes in designing STBCOFDM systems.By following the direct-matrix construction method,we can construct binary extended finite field MRD-STBCs for any number of transmitting antennas.Work uses MRD-STBCs built over Phase-Shift Keying(PSK)modulation to develop an MRD-based STBC-OFDM system.The MRD-based STBC-OFDM system sacrifices minor error performance compared to traditional OSTBC-OFDM but shows improved results against NOSTBC and QOSTBC-OFDM.It also provides 25%higher data-rates than OSTBC-OFDM in configurations that use more than two transmit antennas.The tradeoffs are minor increases in computational complexity and processing delays.展开更多
In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials...In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint (for non-vertical components, see Definition 4) algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.展开更多
In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register (σ-LFSR) which can make full use of the instructions of modern CPUs so that we can find good...In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register (σ-LFSR) which can make full use of the instructions of modern CPUs so that we can find good σ-LFSR with simple structure and fast software implementation. After analysis, we find a class of simple σ-LFSR with maximal period and give an algorithm of searching for those σ-LFSRs. As a result, we provide a new optional fast component in the design of modern wordbased stream ciphers.展开更多
基金This work is supported by project number 1998-015-D00015.
文摘This paper proves that if qn is large enough, for each element a and primitive element b of Fq, there etists a primitive polynomial of degree n ≥5 over the finite field Fq having a as the coefficient of xn-1 and b as the constant term. This proves that if qn is large enongh, for each element a ∈Fq, there exists a primitive polynomial of degree n ≥ 5 over Fq having a as the coefficient of x.
基金supported by the Excellent Foreign Student scholarship program,Sirindhorn International Institute of Technology.
文摘Space-Time Block Coded(STBC)Orthogonal Frequency Division Multiplexing(OFDM)satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel.However,conventional STBCs,including Orthogonal STBCs(OSTBCs),Non-Orthogonal(NOSTBCs),and Quasi-Orthogonal STBCs(QOSTBCs),do not provide both maximal diversity order and unity code rate simultaneously for more than two transmit antennas.This paper targets this problem and applies Maximum Rank Distance(MRD)codes in designing STBCOFDM systems.By following the direct-matrix construction method,we can construct binary extended finite field MRD-STBCs for any number of transmitting antennas.Work uses MRD-STBCs built over Phase-Shift Keying(PSK)modulation to develop an MRD-based STBC-OFDM system.The MRD-based STBC-OFDM system sacrifices minor error performance compared to traditional OSTBC-OFDM but shows improved results against NOSTBC and QOSTBC-OFDM.It also provides 25%higher data-rates than OSTBC-OFDM in configurations that use more than two transmit antennas.The tradeoffs are minor increases in computational complexity and processing delays.
基金partially supported by NKBRPC under Grant No.2011CB302400the National Natural Science Foundation of China under Grant Nos.11001258,60821002,91118001+1 种基金SRF for ROCS,SEMChina-France cooperation project EXACTA under Grant No.60911130369
文摘In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint (for non-vertical components, see Definition 4) algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.
基金the National Natural Science Foundation of China (Grant No. 60503011)the National High-Tech Research and Development Program of China (863 Program) (Grant No. 2006AA01Z425)the National Basic Research Program of China (973 Program) (Grant No. 2007CB807902)
文摘In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register (σ-LFSR) which can make full use of the instructions of modern CPUs so that we can find good σ-LFSR with simple structure and fast software implementation. After analysis, we find a class of simple σ-LFSR with maximal period and give an algorithm of searching for those σ-LFSRs. As a result, we provide a new optional fast component in the design of modern wordbased stream ciphers.