Sequences of Primitive and Non-primitive BCH Codes

ABSTRACT In this work, we introduce a method by which it is established that how a sequence of non-primitive BCH codes can be obtained by a given primitive BCH code. For this, we rush to the out of routine assembling technique of BCH codes and use the structure of monoid rings instead of polynomial rings. Accordingly, it is gotten that there is a sequence { C b j n } 1 ≤ j ≤ m, where b j n is the length of C b j n, of non-primitive binary BCH codes against a given binary BCH code C n of length n. Matlab based simulated algorithms for encoding and decoding for these type of codes are introduced. Matlab provides in routines for construction of a primitive BCH code, but impose several constraints, like degree s of primitive irreducible polynomial should be less than 16. This work focuses on non-primitive irreducible polynomials having degree bs, which go far more than 16.