| Summary: | 博士 === 義守大學 === 資訊工程學系博士班 === 97 === Binary quadratic residue codes are among the most powerful known block codes. This dissertation is focused on the topics of algebraic decoding of binary quadratic residue codes. Two new algebraic decoding schemes for the binary quadratic residue codes are proposed. The key ideals behind these two decoding techniques are the utilization of the inverse-free Berlekamp-Massey algorithm and syndrome polynomial, respectively. In this research, based on ideas of the decoding algorithm suggested by Truong et al. for some quadratic residue codes with irreducible generating polynomials, an algebraic decoder for the (89, 45, 17) binary quadratic residue code with a reducible generating polynomial, the last one not decoded yet of length less than 100, is proposed. It was also verified theoretically for all error patterns within the error-correcting capacity of the code. Moreover, the verification method developed in this research can be extended for all cyclic codes without checking all error patterns by computer simulations.
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