Alternant and BCH codes over certain rings

Artículos de revistas

Date

2003-01-01

Registration in:

Computational & Applied Mathematics. Sociedade Brasileira de Matemática Aplicada e Computacional, v. 22, n. 2, p. 233-247, 2003.

1807-0302

http://hdl.handle.net/11449/22134

10.1590/S0101-82052003000200005

S1807-03022003000200005

S1807-03022003000200005.pdf

8940498347481982

Author

Universidade Estadual Paulista (Unesp)

Universidade Estadual de Campinas (UNICAMP)

Institutions

Universidade Estadual Paulista (Brasil)

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 Zm under Lee metric.

Subjects

codes over rings

Alternant code

BCH codes

Galois extensions of local commutative rings

algebraic decoding

modified Berlekamp-Massey algorithm

errors and erasures decoding

Lee metric

Show full item record