On completely regular and completely transitive supplementary codes
Borges, Joaquim (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Zinoviev, Victor (Russian Academy of Sciences)

Date:	2020
Abstract:	Given a parity-check matrix Hm of a q-ary Hamming code, we consider a partition of the columns into two subsets. Then, we consider the two codes that have these submatrices as parity-check matrices. We say that anyone of these two codes is the supplementary code of the other one. We obtain that if one of these codes is a Hamming code, then the supplementary code is completely regular and completely transitive. If one of the codes is completely regular with covering radius 2, then the supplementary code is also completely regular with covering radius at most 2. Moreover, in this case, either both codes are completely transitive, or both are not. With this technique, we obtain infinite families of completely regular and completely transitive codes which are quasi-perfect uniformly packed.
Grants:	Agencia Estatal de Investigación 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 acceptada per publicar
Subject:	Completely regular codes ; Completely transitive codes ; Hamming codes
Published in:	Discrete Mathematics, Vol. 343, Issue 3 (March 2020) , art. 111732, ISSN 0012-365X

DOI: 10.1016/j.disc.2019.111732

Postprint 22 p, 346.3 KB

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