Abstract
Error-control coding — the magic technology that enables reliable digital communications — is described usually in terms of some special mathematics. The purpose of this chapter is to present briefly these mathematical tools. Some basic structures of algebra, such as groups, rings, fields, and vector spaces, are introduced. These mathematical entities will play an important role in error-control coding theory as well as in encoder-decoder implementations. Only those properties of algebra which are needed for the study of error-correction codes are discussed in any detail. It is assumed that the reader already has some familiarity with these topics. Hence, the discussion given here is not intended to be either systematic or complete.
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