Basics on Error Control

Abstract

The basic idea of coding is to introduce redundancy that can be utilized to detect and, for some applications, correct errors that has occurred during a transmission over a channel. We will restrict our attention to encoding into vectors of symbols from a finite field ofqelements, whereqis some prime power; the most important case is q =2. The reason for this restriction is that we can make use of the mathematical structure and extensive theory for vector spaces. However, it is quite possible to consider more general encodings.