An association between primitive and non-primitive BCH codes using monoid rings.

BCH codes are one of the most important classes of cyclic codes for error correction. In this study, we generalize BCH codes using monoid rings instead of a polynomial ring over the binary field F. We show the existence of a non-primitive binary BCH code C of length bn, corresponding to a given length n binary BCH code C. The value of b is investigated for which the existence of the non-primitive BCH code C is assured. It is noticed that the code C is embedded in the code C. Therefore, encoding and decoding of the codes C and C can be done simultaneously. The data transmitted by C can also be transmitted by C. The BCH code C has better error correction capability whereas the BCH code C has better code rate, hence both gains can be achieved at the same time. [ABSTRACT FROM AUTHOR]