A decoding method of an n length binary BCH code through (n+1)n length binary cyclic code

Author(s)

Shah, Tariq ; Khan, Mubashar ; De Andrade, Antonio A.

• Document type: Journal article
• Source: Anais da Academia Brasileira de Ciências; v. 85, n. 3, p. 10-pg., 2013-09-01.

Abstract

For a given binary BCH code C-n of length n = 2(s) - 1 generated by a polynomial g(x) is an element of F-2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x(1/2)) is an element of F-2[x 1/2 Z >= 0] of degree 2r. However, it does exist a binary cyclic code C(n+l)n of length (n + 1)n such that the binary BCH code C-n is embedded in C(n+1)n. Accordingly a high code rate is attained through a binary cyclic code C(n+1)n for a binary BCH code C-n. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code C-n through the decoding of a binary cyclic code C(n+1)n, while the codes C-n and C(n+1)n have the same minimum hamming distance. (AU)

• FAPESP's process: 11/03441-2 - Codes and lattices with applications
• Grantee: Antonio Aparecido de Andrade
• Support Opportunities: Research Grants - Visiting Researcher Grant - International