Constructions of nonlinear covering codes

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1997Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Information Theory, volume 43, pages 1,639-1,647 (issn: 0018-9448,

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Authors: Alexander A. Davydov;

doi: 10.1109/18.623166

Constructions of nonlinear covering codes

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Abstract

Summary: Constructions of nonlinear covering codes are given. Using any nonlinear starting code of covering radius \(R\geq 2\) these constructions form an infinite family of codes with the same covering radius. A nonlinear code is treated as a union of cosets of a linear code. New infinite families of nonlinear covering codes are obtained. Concepts of \(R,l\)-objects, \(R,l\)-partitions, and \(R,l\)-length are described for nonlinear codes.

Related Organizations

Russian Academy of Sciences
Russian Federation

Keywords

covering radius, covering codes, Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory, nonlinear codes

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