Alternant and BCH codes over certain rings
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Springer
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Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x(s) - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore, we address the construction of BCH codes over Z(m) under Lee metric.
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codes over rings, alternant codes, BCH codes, Galois extensions of local commutative rings, algebraic decoding, modified Berlekamp-Massey algorithm, errors and erasures decoding, Lee metric
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Inglês
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Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 22, n. 2, p. 233-247, 2003.
