For a given binary BCH code Cn
of length n = 2s - 1 generated by a polynomial 
of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial 
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.
BCH code; binary cyclic code; binary Hamming code; decoding algorithm