Abstract This paper presents a construction of 2 (2 n-1,n,λ) designs and gives the polynomial description of this class of designs.The construction applies to the cases of all integer n ≥2.
Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vec...Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.展开更多
Fully diverse unitary space-time codes are useful in multiantenna communications, especially in multiantenna differential modulation. Recently, two constructions of parametric fully diverse unitary space-time codes fo...Fully diverse unitary space-time codes are useful in multiantenna communications, especially in multiantenna differential modulation. Recently, two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced. We propose a new construction method based on the constructions. In the present paper, fully diverse codes for systems of odd prime number antennas are obtained from this construction. Space-time codes from present construction are found to have better error performance than many best known ones.展开更多
Constant composition codes(CCCs)are a new generalization of binary constant weight codes and have attracted recent interest due to their numerous applications. In this paper, a new combinatorial approach to the constr...Constant composition codes(CCCs)are a new generalization of binary constant weight codes and have attracted recent interest due to their numerous applications. In this paper, a new combinatorial approach to the construction of CCCs is proposed, and used to establish new optimal CCCs.展开更多
Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error p...Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error positions (the roots of error locator polynomials). Several fast root-finding algorithms for polynomials over finite fields have been proposed. In this paper we give a generalization of the Goertzel algorithm. Our algorithm is suitable for the parallel hardware implementation and the time of multiplications used is restricted by a constant.展开更多
文摘Abstract This paper presents a construction of 2 (2 n-1,n,λ) designs and gives the polynomial description of this class of designs.The construction applies to the cases of all integer n ≥2.
基金supported by National Natural Science Foundation of China (Grant No. 10871068)
文摘Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
基金supported by National Natural Science Foundation of China (Grant No. 60673074)
文摘Fully diverse unitary space-time codes are useful in multiantenna communications, especially in multiantenna differential modulation. Recently, two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced. We propose a new construction method based on the constructions. In the present paper, fully diverse codes for systems of odd prime number antennas are obtained from this construction. Space-time codes from present construction are found to have better error performance than many best known ones.
基金the National Natural Foundation of China (Grant Nos. 10671140, 10626038)
文摘Constant composition codes(CCCs)are a new generalization of binary constant weight codes and have attracted recent interest due to their numerous applications. In this paper, a new combinatorial approach to the construction of CCCs is proposed, and used to establish new optimal CCCs.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 60433050, 90607005)
文摘Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error positions (the roots of error locator polynomials). Several fast root-finding algorithms for polynomials over finite fields have been proposed. In this paper we give a generalization of the Goertzel algorithm. Our algorithm is suitable for the parallel hardware implementation and the time of multiplications used is restricted by a constant.
