2007•Unpublished venueRequires access

A New Approach to Decoding of BCH and Reed-Solomon Codes Using Syzygy

Il‐Ho Kim, Hyoung J. Ko

Abstract

A new approach to decoding of BCH and Reed-Solomon codes by using syzygy modules of matricies is introduced. The decoding procedure reduces the computational complexity roughly by half by introducing syzygy modules since the number of variables in each step is reduced by half. The decoding of binary BCH codes can be viewed as the special case of the decoding of nonbinary BCH or Reed-Solomon codes.

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Key concepts: BCH code, Hilbert's syzygy theorem, Decoding methods, Reed–Solomon error correction, Berlekamp–Welch algorithm, List decoding, Mathematics, Computer science