Loading...
2^n bordered constructions of self-dual codes from group rings
Dougherty, Steven Gildea, Joe Kaya, Abidin
Dougherty, Steven
Gildea, Joe
Kaya, Abidin
Citations
Altmetric:
Advisors
Editors
Other Contributors
EPub Date
Publication Date
2020-08-04
Submitted Date
Collections
Files
Loading...
Main Article
Adobe PDF, 398.54 KB
Other Titles
Abstract
Self-dual codes, which are codes that are equal to their orthogonal, are a widely studied family of codes.
Various techniques involving circulant matrices and matrices from group rings have been used to construct
such codes. Moreover, families of rings have been used, together with a Gray map, to construct binary
self-dual codes. In this paper, we introduce a new bordered construction over group rings for self-dual
codes by combining many of the previously used techniques. The purpose of this is to construct self-dual
codes that were missed using classical construction techniques by constructing self-dual codes with different
automorphism groups. We apply the technique to codes over finite commutative Frobenius rings of characteristic
2 and several group rings and use these to construct interesting binary self-dual codes. In particular, we construct
some extremal self-dual codes length 64 and 68, constructing 30 new extremal self-dual codes of length 68.
Citation
Dougherty, S., Gildea, J. & Kaya, A. (2020). 2^n Bordered Constructions of Self-Dual codes from Group Rings. Finite Fields and Their Applications, 67, 101692. https://doi.org/10.1016/j.ffa.2020.101692
Publisher
Elsevier
Journal
Finite Fields and Their Applications
Research Unit
PubMed ID
PubMed Central ID
Type
Article
Language
Description
Series/Report no.
ISSN
1071-5797