Composite constructions of self-dual codes from group rings and new extremal self-dual binary codes of length 68
| Autor: | Steven T. Dougherty, Adrian Korban, Joe Gildea, Abidin Kaya |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Computer Networks and Communications Applied Mathematics Binary image Binary number 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Microbiology Dual (category theory) Combinatorics 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Binary code Mathematics Group ring |
| Zdroj: | Advances in Mathematics of Communications. 14:677-702 |
| ISSN: | 1930-5338 |
| DOI: | 10.3934/amc.2020037 |
| Popis: | We describe eight composite constructions from group rings where the orders of the groups are 4 and 8, which are then applied to find self-dual codes of length 16 over \begin{document}$ \mathbb{F}_4 $\end{document} . These codes have binary images with parameters \begin{document}$ [32,16,8] $\end{document} or \begin{document}$ [32,16,6] $\end{document} . These are lifted to codes over \begin{document}$ \mathbb{F}_4+u\mathbb{F}_4 $\end{document} , to obtain codes with Gray images of extremal self-dual binary codes of length 64. Finally, we use a building-up method over \begin{document}$ \mathbb{F}_2+u\mathbb{F}_2 $\end{document} to obtain new extremal binary self-dual codes of length 68. We construct 11 new codes via the building-up method and 2 new codes by considering possible neighbors. |
| Databáze: | OpenAIRE |
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