Alternant and BCH codes over certain rings
Computational & Applied Mathematics. Sociedade Brasileira de Matemática Aplicada e Computacional, v. 22, n. 2, p. 233-247, 2003.
Palazzo Jr., R.
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 Zm under Lee metric.