BCH Codes Decoder Based on Euclid Algorithm

B I Filippov,
Novosibirsk State Technical University, Department of Information Security, Novosibirsk City, Russian Federation

DOI: 10.36724/2664-066X-2021-7-2-14-17

SYNCHROINFO JOURNAL. Volume 7, Number 2 (2021). P. 14-17.


In the process of algebraic decoding of BCH codes over the field GF(q) with the word length n = qm-1, correcting t errors, both in the time and frequency domains, it is necessary to find the error locator polynomial ?(x) as the least polynomial for which the key equation. Berlekamp proposed a simple iterative scheme, which was called the Berlekamp-Messi algorithm, and is currently used in most practical applications. Comparative statistical tests of the proposed decoder and decoder using the Berlikamp-Messi algorithm showed that they differ slightly in decoding speed. The proposed algorithm is implemented in the environment in Turbo Pascal and can be used for the entire family of BCH codes by replacing the primitive Galois polynomial.

Keywords: Berlekamp-Messi algorithm, Euclidean algorithm, BCH codes, Galois polynomial, decoder.


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