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Bordered Constructions of Self-Dual Codes from Group Rings and New Extremal Binary Self-Dual Codes
Dougherty, Steven Gildea, Joe Kaya, Abidin Korban, Adrian Tylyshchak, Alexander Yildiz, Bahattin
Dougherty, Steven
Gildea, Joe
Kaya, Abidin
Korban, Adrian
Tylyshchak, Alexander
Yildiz, Bahattin
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Publication Date
2019-02-22
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Abstract
We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring $\F_2+u\F_2$, using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.
Citation
Dougherty, S. T., Gildea, J., Korban, A., Kaya, A., Tylyshchak, A., & Yildiz, B. (2019). Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes. Finite Fields and their Applications, 57, 108-127
Publisher
Elsevier
Journal
Finite Fields and Their Applications
Research Unit
DOI
10.1016/j.ffa.2019.02.004
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PubMed Central ID
Type
Article
Language
en
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ISSN
1071-5797