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Elements of Algebraic Coding Systems by Valdemar Cardoso da Rocha, Jr.

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Chapter 3

CYCLIC CODES

Among the codes in the class of block codes cyclic codes are the most important from the point of view of practical engineering applications (Clark and Cain 1981, p.333). Cyclic codes are used in communication protocols (A, Györfi, and Massey 1992), in music CDs, in magnetic recording (Immink 1994), etc. This is due to their structure being based on discrete mathematics, which allows a considerable simplification in the implementation of encoders and decoders. The formal treatment of cyclic codes is done in terms of polynomial rings, with polynomial coefficients belonging to a Galois field GF(q), modulo xn 1, where n denotes the block length (Berlekamp 1968, p.119). However, a simple way to define cyclic codes is as follows. ...

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