Open AccessSequences of Primitive and Non-primitive BCH Codes
Author(s) -
A. S. Ansari,
T. Shah,
Zia Ur-Rahman,
Antonio Aparecido de Andrade
Publication year - 2018
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2018.019.02.369
Subject(s) - bch code , primitive polynomial , polynomial , sequence (biology) , mathematics , discrete mathematics , binary number , decoding methods , degree (music) , code (set theory) , combinatorics , computer science , algorithm , arithmetic , finite field , physics , biology , genetics , mathematical analysis , set (abstract data type) , acoustics , programming language
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.