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Constructions of nonlinear covering codes

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1 Author(s)
Davydov, A.A. ; Inst. of Problems of Inf. Transmission, Acad. of Sci., Moscow, Russia

Constructions of nonlinear covering codes are given. Using any nonlinear starting code of covering radius R⩾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

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Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 5 )