A method for improving the code rate and error correction capability of a cyclic code

Nenhuma Miniatura disponível

Data

2013-07-01

Autores

Shah, Tariq
Amanullah,
de Andrade, Antonio Aparecido [UNESP]

Título da Revista

ISSN da Revista

Título de Volume

Editor

Resumo

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for the exchange, processing and storage of digital information in the different spheres. In this paper, we explore a way to achieve this goal. For given positive integers n,r, we establish that corresponding to a binary cyclic code C0[n,n-r], there is a binary cyclic code C[(n+1)3k-1,(n+1)3k-1-3kr], where k is a nonnegative integer, which plays a role in enhancing code rate and error correction capability. In the given scheme, the new code C is in fact responsible to carry data transmitted by C0. Consequently, a codeword of the code C0 can be encoded by the generator matrix of C and therefore this arrangement for transferring data offers a safe and swift mode. © 2013 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

Descrição

Palavras-chave

Binary cyclic code, Binary Hamming code, Polynomial ring, Semigroup ring

Como citar

Computational and Applied Mathematics, v. 32, n. 2, p. 261-274, 2013.