A decoding procedure which improves code rate and error corrections
Nenhuma Miniatura disponível
Data
2012
Autores
Shah, Tariq
Andrade, Antonio Aparecido de [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Resumo
Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\in \mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\in \mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\frac{1}{3^{k}}})\in \mathbb{F}_{2}[X;\frac{1}{3^{k}}\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\in \mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.
Descrição
Palavras-chave
Semigroup ring, Binary cyclic code, Binary Hamming code, Decoding principle, Code rate, Error correction
Como citar
Journal of Advanced Research in Applied Mathematics, v. 4, n. 4, p. 37-50, 2012.