Quaternary group ring codes : ranks, kernels and self-dual codes
Dougherty, Steven T. (University of Scranton. Department of Mathematics)
Fernández Córdoba, Cristina (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Ten-Valls, Roger (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Yildiz, Bahattin (Northern Arizona University. Department of Mathematics and Statistics)

Data:	2020
Descripció:	14 pàg.
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.
Ajuts:	Ministerio de Economía y Competitividad TIN2016-77918-P
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Matèria:	Dicyclic ; Dihedral ; Group ring codes ; Kernel ; Quaternary codes ; Rank ; Self-dual Codes ; Algebra and Number Theory ; Computer Networks and Communications ; Discrete Mathematics and Combinatorics ; Applied Mathematics
Publicat a:	Advances in mathematics of communications, Vol. 14, issue 2 (May 2020) , p. 319-332, ISSN 1930-5338

DOI: 10.3934/amc.2020023

Preprint 15 p, 455.1 KB

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