New Self-dual Codes from 2 x 2 block circulant matrices, Group Rings and Neighbours of Neighbours
Affiliation
University of Chester; Harmony Public Schools; Uzhgorod National UniversityPublication Date
2021-09-01Metadata
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In this paper, we construct new self-dual codes from a construction that involves a unique combination; 2 x 2 block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, specified in this paper, where this new construction yields self-dual codes. The theory is supported by the construction of self-dual codes over the rings F2, F2+uF2 and F4+uF4. Using extensions and neighbours of codes, we construct 32 new self-dual codes of length 68. We construct 48 new best known singly-even self-dual codes of length 96.Citation
Gildea, J., Kaya, A., Roberts, A., Taylor, R., & Tylyshchak, A. (2023). New self-dual codes from 2 x 2 block circulant matrices, group rings and neighbours of neighbours. Advances in Mathematics of Communications, 17(5), 1086-1100. https://doi.org/10.3934/amc.2021039Additional Links
https://www.aimsciences.org/article/doi/10.3934/amc.2021039Type
ArticleDescription
This document is the Accepted Manuscript version of a published work that appeared in final form in Advances in Mathematics of Communications. To access the final edited and published work see https://www.aimsciences.org//article/doi/10.3934/amc.2021039http://dx.doi.org/10.3934/amc.2021039ISSN
1930-5346EISSN
1930-5338Scopus Count
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Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/4.0/