Per citar aquest document:
Survey on Z₂Z₄-additive codes
Borges, J. (Joaquim) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Pujol Capdevila, Jaume (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Data: 2014
Resum: A code C is Z₂Z₄-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y ) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of Z₂Z₄-additive codes under an extended Gray map are called Z₂Z₄-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 shown and standard forms for generator and parity-check matrices are given, defining the appropriate concept of duality. The main results on Z₂Z₄-additive self-dual and Z₂Z₄-additive formally self-dual codes are also presented, as well as, the results on the invariants rank and dimension of the kernel for these codes are given. Several families of important binary codes fall in the class of Z₂Z₄-linear codes. In this survey, we review characterizations, properties and constructions of perfect and extended perfect Z₂Z₄-linear codes, Hadamard Z₂Z₄-linear codes, Reed-Muller Z₂Z₄-linear codes, maximum distance separable Z₂Z₄-linear codes, and Preparata-like and Kerdock-like Z₂Z₄-linear codes. Finally, applications of Z₂Z₄-additive codes to steganography are also presented.
Nota: Número d'acord de subvenció MICINN/TIN2013-40524-P
Nota: Número d'acord de subvenció AGAUR/2014/SGR-691
Drets: Tots els drets reservats
Llengua: Anglès
Document: bookPart
Publicat a: Proceedings of the contact forum Galois geometries and applications, 2014

49 p, 278.9 KB

El registre apareix a les col·leccions:
Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Enginyeries > Combinatorics, Coding and Security Group (CCSG)
Contribucions a jornades i congressos > Ponències i comunicacions

 Registre creat el 2015-11-06, darrera modificació el 2016-04-19

   Favorit i Compartir