Z2Z4-linear codes: generator matrices and duality

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dc.creatorBorges, J.
dc.creatorFernandez, C.
dc.creatorPujol, J.
dc.creatorRifa, J.
dc.creatorVillanueva, M.
dc.date2007-10-05
dc.date.accessioned2026-07-07T08:34:21Z
dc.date.available2026-07-07T08:34:21Z
dc.descriptionA code ${\cal C}$ is $\Z_2\Z_4$-additive if the set of coordinates can be partitioned into two subsets $X$ and $Y$ such that the punctured code of ${\cal C}$ by deleting the coordinates outside $X$ (respectively, $Y$) is a binary linear code (respectively, a quaternary linear code). In this paper $\Z_2\Z_4$-additive codes are studied. Their corresponding binary images, via the Gray map, are $\Z_2\Z_4$-linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes, for these codes the fundamental parameters are found and standard forms for generator and parity check matrices are given. For this, the appropriate inner product is deduced and the concept of duality for $\Z_2\Z_4$-additive codes is defined. Moreover, the parameters of the dual codes are computed. Finally, some conditions for self-duality of $\Z_2\Z_4$-additive codes are given.
dc.descriptionThis paper will be submitted to IEEE Trans. on Inform. Theory
dc.identifierhttps://arxiv.org/abs/0710.1149
dc.identifierhttp://arxiv.org/abs/0710.1149
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139410
dc.subjectInformation Theory
dc.subjectDiscrete Mathematics
dc.subjectCombinatorics
dc.subject94B25; 11T71
dc.titleZ2Z4-linear codes: generator matrices and duality
dc.typetext

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