Construction and decoding of BCH codes over chain of commutative rings

Autor(es)

Shah, Tariq ; Qamar, Attiq ; de Andrade, Antonio Aparecido

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICAL SCIENCES; v. 6, n. 1, p. 14-pg., 2012-12-01.

Resumo

In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A(0) subset of A(1)subset of . . . subset of A(t-1). A(t) be a chain of unitary commutative rings, where each A(i) is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K-0 subset of K-1 subset of . . . subset of Kt-1 subset of K-t (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A(i)(*)and K-i(*) are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A(i)(*) and K-i(*) for each i, where 0 <= i <= t. By the construction of BCH codes, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH code concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH codes at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings. (AU)

• Processo FAPESP: 11/03441-2 - Códigos e reticulados com aplicações
• Beneficiário: Antonio Aparecido de Andrade
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 07/56052-8 - Teoria da informação e códigos
• Beneficiário: Sueli Irene Rodrigues Costa
• Modalidade de apoio: Auxílio à Pesquisa - Temático