Quasi-cyclic codes as cyclic codes over a family of local rings

Steven T. Dougherty, Cristina Fernández-Córdoba, Roger Ten-Valls

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Resum

© 2016 Elsevier Inc. All rights reserved. We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic.
Idioma originalAnglès
Pàgines (de-a)138-149
RevistaFinite Fields and Their Applications
Volum40
DOIs
Estat de la publicacióPublicada - 1 de jul. 2016

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