Alternant and BCH codes over certain rings

Abstract

Abstract.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.Mathematical subject classification: 11T71, 94B05, 94B40.

Goppa and Srivastava codes over finite rings

“…Linear codes over local finite commutative rings with identity have been discussed in papers by Andrade [1], [2], [3] where it was extended the notion of Hamming, Reed-Solomon, BCH and alternant codes over these rings.…”

On Goppa and Srivastava codes over finite rings

“…In this section we review a construction technique of BCH and alternant codes [2], [3] over local finite rings.…”

Reticulados, projeções e aplicações à teoria da informação

“…Seja r = (0, 7, 4, 8, 0, 12, 0) t . Utilizando o algoritmo em [AIPJ03], obtemos que o ponto de C mais próximo de r = (0, 3, 0, 0, 0, 0, 0) é x = (0, 0, 0, 0, 0, 0, 0). Assim, na notação da Proposição 2.2.5,…”