Information Theory, Coding and Cryptography

Chapter 5

Linear Block Codes

5.1  INTRODUCTION

With the advent of digital computers and digital data communication systems, information is coded in binary digits ‘0’ or ‘1’. This binary information sequence is segmented into message blocks of fixed length in block coding. Each message block consists of k-information bits and is denoted by u. Thus, there may be 2^k distinct messages. According to certain rules, this message u is then transformed into a binary n-tuple v, with n > k. The binary n-tuple v is referred to as the code vector (or code word) of the message u. Thus, there may be 2^k distinct code vectors corresponding to 2^k distinct possible message vectors. The set of these 2^k distinct code vectors is known as block code. A desirable property ...