On Z2Z4-additive complementary dual codes and related LCD codes
Benbelkacem, N. (University of Science and Technology Houari Boumediene. Faculty of Mathematics)
Borges, J. (Joaquim), (Joaquim), dir. (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
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)

Date:	2020
Abstract:	Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. These codes are additive, in the sense that they are additive subgroups, rather than linear as they are not vector spaces over some finite field. We study the structure of these codes and we use the canonical Gray map from this space to the Hamming space to construct binary LCD codes in certain cases. We give examples of such binary LCD codes which are distance-optimal, i. e. , they have the largest minimum distance among all binary LCD codes with the same length and dimension.
Grants:	Ministerio de Ciencia e Innovación TIN2016-77918-P
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Subject:	Complementary dual ; Gray map ; LCD codes ; ZZ-additive codes ; Theoretical Computer Science ; Algebra and Number Theory ; Engineering(all) ; Applied Mathematics
Published in:	Finite Fields and their Applications, Vol. 62 (Feb. 2020) , art. 101622, ISSN 1090-2465

DOI: 10.1016/j.ffa.2019.101622

Preprint 19 p, 415.1 KB

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