Discrete Mathematics and Combinatorics

Chapter 13

Coding Theory

Learning Objectives

On completing this chapter, you will be able to:

• define an encoding function

• define the minimum distance of a code

• calculate the minimum distance of a given code

• define and identify group codes

• calculate the maximum number of errors that can be detected by a given code

• design codes that would detect a given number or fewer errors

• calculate the maximum number of errors that can be corrected by a given code

• decode strings using maximum likelihood procedure

• design codes that would correct a given number or fewer errors

• decode strings using the concept of a syndrome

13.1 INTRODUCTION AND PRELIMINARIES

Example 13.1

A globe-trotting CEO of a firm has four offices in India at Chennai, Mumbai, Kolkata ...