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New Self-Dual and Formally Self-Dual Codes from Group Ring Constructions
Dougherty, Steven Gildea, Joe Kaya, Abidin Yildiz, Bahattin
Dougherty, Steven
Gildea, Joe
Kaya, Abidin
Yildiz, Bahattin
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Publication Date
2019-08-31
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Abstract
In this work, we study construction methods for self-dual and formally self-dual
codes from group rings, arising from the cyclic group, the dihedral group, the dicyclic
group and the semi-dihedral group. Using these constructions over the rings $_F2 +uF_2$
and $F_4 + uF_4$, we obtain 9 new extremal binary self-dual codes of length 68 and 25
even formally self-dual codes with parameters [72,36,14].
Citation
Dougherty, S. T., Gildea, J., Kaya, A., & Yildiz, B. (2019). New self-dual and formally self-dual codes from group ring constructions. Advances in Mathematics of Communications, 14(1), 11-22.
Publisher
American Institute of Mathematical Sciences
Journal
Advances in Mathematics of Communications
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Type
Article
Language
en
Description
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Advances in Mathematics of Communications following peer review. The definitive publisher-authenticated version Dougherty, S., Gildea, J., Kaya, A., & Yildiz, B. (2019). New Self-Dual and Formally Self-Dual Codes from Group Ring Constructions. Advances in Mathematics of Communications will be available when published online at http://www.aimsciences.org/journal/1930-5346
Series/Report no.
ISSN
1930-5346
EISSN
1930-5338