Information Theory, Coding and Cryptography

Chapter 7

BCH Codes

7.1  INTRODUCTION

A large class of powerful random-error-correcting cyclic codes had been formed by BCH codes that made remarkable generalization of the Hamming codes for multiple error correction. BCH codes were invented in 1959 by Alexis Hocquenghem, and independently in 1960 by Raj Chandra Bose and Dwijendra Kumar Ray-Chaudhuri. Thus the code has been named as BCH (Bose Chaudhuri Hocquenghem) code. The cyclic structure of this code was observed and subsequently generalization of binary BCH codes to codes of p^m symbols (p is a prime) was done. However, in this chapter, the discussion will be confined to mainly binary BCH codes.

7.2  PRIMITIVE ELEMENTS

For any positive integers m (m ≥ 3) and t (t < 2^m – 1), there exist a ...