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

Shah, TariqKhan, MubasharDe Andrade, Antonio Aparecido [UNESP]2014-05-272014-05-272013-09-01Anais da Academia Brasileira de Ciencias, v. 85, n. 3, p. 863-872, 2013.0001-37651678-2690http://hdl.handle.net/11449/76462For a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of degree 2r. However, it does exist a binary cyclic code C(n+1)n of length (n + 1)n such that the binary BCH code Cn 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 Cn. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code Cn through the decoding of a binary cyclic code C(n+1)n, while the codes Cn and C(n+1)n have the same minimum hamming distance.863-872engBCH codeBinary cyclic codeBinary Hamming codeDecoding algorithmA decoding method of an n length binary BCH code through (n + 1)n length binary cyclic codeArtigo10.1590/S0001-37652013000300002S0001-37652013000300002S0001-37652013000300863WOS:000324948400002Acesso aberto2-s2.0-848842357762-s2.0-84884235776.pdf8940498347481982