Advanced Engineering Mathematics, 7th Edition

8.15 Error-Correcting Code

INTRODUCTION

In contrast to the last section, there is no connotation of secretiveness to the word code as used in this section. We are going to examine briefly the concept of digital communication, say, communication between a satellite and a computer. As a consequence, we will deal only with matrices whose entries are binary digits, namely, 0 s and 1s. When adding and multiplying such matrices, we will use arithmetic modulo 2. This arithmetic is defined by the addition and multiplication tables

Fundamental properties such as the commutative and associative laws hold in this system. The only notable exception here ...