## 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 ...