Quaternary group ring codes: Ranks, kernels and self-dual codes

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

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Resum

We study G-codes over the ring Z4, which are codes that are held invariant by the action of an arbitrary group G. We view these codes as ideals in a group ring and we study the rank and kernel of these codes. We use the rank and kernel to study the image of these codes under the Gray map. We study the specific case when the group is the dihedral group and the dicyclic group. Finally, we study quaternary self-dual dihedral and dicyclic codes, tabulating the many good self-dual quaternary codes obtained via these constructions, including the octacode.

Idioma originalAnglès
Pàgines (de-a)319-332
Nombre de pàgines14
RevistaAdvances in Mathematics of Communications
Volum14
Número2
DOIs
Estat de la publicacióPublicada - 2020

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