A BCH code and a sequence of cyclic codes

• Main Author: Andrade, Antonio Aparecido de [UNESP]
• Publication Date: 2014
• Other Authors: Shah, Tariq, Khan, Mubashar
• Format: Article
• Language: eng
• Source: Repositório Institucional da UNESP
• Download full: http://www.m-hikari.com/ija/ija-2014/ija-9-12-2014/index.html; http://hdl.handle.net/11449/122329
• topic: Cyclic code; BCH code; decoding procedure

This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the binary cyclic code Cm 2m−1(n+1)n has length 2m−1(n + 1)n and is generated by a generalized polynomial g(x 1 2m ) ∈ F2[x, 1 2m Z≥0] of degree 2mr. Furthermore, C0 n is embedded in Cm 2m−1(n+1)n and Cm 2m−1(n+1)n is embedded in Cm+1 2m(n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {Cm 2m−1(n+1)n}m≥1 of binary cyclic codes, having the same code rate.