1974•Proceedings of the Institution of Electrical EngineersRequires access

Class of linear binary codes

A.A. Hashim, A.G. Constantinides

Abstract

A class of algebraic linear codes is introduced in which the parity-check matrix of the code is constructed by using a subset of the Abelian group of Walsh functions. These codes meet the Helgert and Stinaff upper bounds on minimum Hamming distance, and all the codes of this class are easily decodable by a one-step majority-logic algorithm.

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Available abstract

Key concepts: Linear code, Hamming code, Reed–Muller code, Block code, Raptor code, Hamming distance, Mathematics, Hamming weight