On the algebraic representation of selected optimal non-linear binary codes

Marcus Greferath*, Jens Zumbraegel

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

Revisiting an approach by Conway and Sloane we investigate a collection of optimal non-linear binary codes and represent them as (non-linear) codes over Z(4). The Fourier transform will be used in order to analyze these codes, which leads to a new algebraic representation involving subgroups of the group of units in a certain ring.

One of our results is a new representation of Best's (10, 40, 4) code as a coset of a subgroup in the group of invertible elements of the group ring Z(4)[Z(5)]. This yields a particularly simple algebraic decoding algorithm for this code.

The technique at hand is further applied to analyze Julin's (12, 144, 4) code and the (12, 24, 12) Hadamard code. It can also be used in order to construct a (non-optimal) binary (14, 56, 6) code.

Original languageEnglish
Title of host publication2012 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT)
PublisherIEEE
Pages3115-3119
Number of pages5
ISBN (Electronic)978-1-4673-2579-0
ISBN (Print)978-1-4673-2580-6
DOIs
Publication statusPublished - 2012
MoE publication typeA4 Article in a conference publication
EventIEEE International Symposium on Information Theory - Cambridge, Morocco
Duration: 1 Jul 20126 Jul 2012

Publication series

NameIEEE International Symposium on Information Theory
PublisherIEEE
Name Information Theory Proceedings (ISIT)
PublisherIEEE
ISSN (Print)2157-8095
ISSN (Electronic)2157-8117

Conference

ConferenceIEEE International Symposium on Information Theory
CountryMorocco
CityCambridge
Period01/07/201206/07/2012

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