Constructions of Nonequivalent Fp-Additive Generalised Hadamard Codes

Steven T. Dougherty, Josep Rifa, Merce Villanueva

Research output: Chapter in BookChapterResearchpeer-review

Abstract

A subset of a vector space Fnq is K-additive if it is a linear space over the subfield K C Fq. Let q = pe, p prime, and e > 1. Bounds on the rank and dimension of the kernel of generalised Hadamard (GH) codes which are Fp-additive are established. For specific ranks and dimensions of the kernel within these bounds, Fp-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 Fp-additive GH code for all allowable ranks and dimensions of the kernel between these bounds. Finally, we also prove that these codes are selforthogonal with respect to the trace Hermitian inner product, and generate pure quantum codes.

Original languageEnglish
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages150-155
Number of pages6
ISBN (Electronic)9781728164328
DOIs
Publication statusPublished - Jun 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2020-June
ISSN (Print)2157-8095

Fingerprint

Dive into the research topics of 'Constructions of Nonequivalent F<sub>p</sub>-Additive Generalised Hadamard Codes'. Together they form a unique fingerprint.

Cite this