Sequences of Primitive and Non-primitive BCH Codes


  • A. S. Ansari
  • T. Shah
  • Zia Ur-Rahman
  • Antonio A. Andrade Departamento de Matemática, Ibilce - Unesp, São José do Rio Preto - SP



Monoid ring, BCH codes, primitive polynomial, non-primitive polynomial.


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 $\{C_{b^{j}n}\}_{1\leq j\leq m}$, 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 built 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.

Author Biography

Antonio A. Andrade, Departamento de Matemática, Ibilce - Unesp, São José do Rio Preto - SP

Departamento de Matemática


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How to Cite

Ansari, A. S., Shah, T., Ur-Rahman, Z., & Andrade, A. A. (2018). Sequences of Primitive and Non-primitive BCH Codes. Trends in Computational and Applied Mathematics, 19(2), 369.



Original Article