1968•IEEE Transactions on Information TheoryRequires access

Polynomial codes

Tadao Kasami, Shu Lin, W. W. Peterson

Abstract

A class of cyclic codes is introduced by a polynomial approach that is an extension of the Mattson-Solomon method and of the Muller method. This class of codes contains several important classes of codes as subclasses, namely, BCH codes, Reed-Solomon codes, generalized primitive Reed-Muller codes, and finite geometry codes. Certain fundamental properties of this class of codes are derived. Some subclasses are shown to be majority-logic decodable.

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Key concepts: Reed–Muller code, BCH code, Block code, Reed–Solomon error correction, Linear code, Mathematics, Expander code, Discrete mathematics