Rank and kernel of additive generalised Hadamard codes
Dougherty, Steven T. (University of Scranton. Department of Mathematics)
Rifà i Coma, Josep (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)
Villanueva, M. (Mercè) (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions)

Date:	2021
Abstract:	A subset of a vector space Fn q is additive if it is a linear space over the field Fp, where q = pe, p prime, and e > 1. Bounds on the rank and dimension of the kernel of additive generalised Hadamard (additive GH) codes are established. For specific ranks and dimensions of the kernel within these bounds, additive GH codes are constructed. Moreover, for the case e = 2, it is shown that the given bounds are tight and it is possible to construct an additive GH code for all allowable ranks and dimensions of the kernel between these bounds. Finally, we also prove that these codes are self-orthogonal with respect to the trace Hermitian inner product, and generate pure quantum codes.
Grants:	Ministerio de Ciencia e Innovación PID2019-104664GB-I00
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Additive code ; Generalised Hadamard code ; Generalised Hadamard matrix ; Kernel ; Nonlinear code ; Rank
Published in:	IEEE Transactions on Information Theory, Vol. 67, Issue 11 (November 2021) , p. 7210-7220, ISSN 1557-9654

DOI: 10.1109/TIT.2021.3100433

Postprint 13 p, 516.1 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Engineering > Combinatorics, Coding and Security Group (CCSG)
Articles > Research articles
Articles > Published articles