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Testing algebraic geometric codes 被引量:2
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作者 CHEN Hao Software Engineering Institute, East China Normal University, Shanghai 200062, China 《Science China Mathematics》 SCIE 2009年第10期2171-2176,共6页
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
关键词 number theory of finite field property testing algebraic geometric codes 94b35 94B99
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The generalized Goertzel algorithm and its parallel hardware implementation
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作者 CHEN Hao CHEN GongLiang LI JianHua 《Science China Mathematics》 SCIE 2008年第1期37-41,共5页
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
关键词 number theory of finite field RS and BCH decoding normal base the Goertzel algorithm 94b35 94-30
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