New Self-dual Codes from 2 x 2 block circulant matrices, Group Rings and Neighbours of Neighbours
AffiliationUniversity of Chester; Harmony Public Schools; Uzhgorod National University
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AbstractIn this paper, we construct new self-dual codes from a construction that involves a unique combination; $2 \times 2$ 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 $\FF_2$, $\FF_2+u\FF_2$ and $\FF_4+u\FF_4$. 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.
CitationGildea, J., Kaya, A., Roberts, A., Taylor, R., & Tylyshchak, A. (2021 - forthcoming). New self-dual codes from 2 x 2 block circulant matrices, group rings and neighbours of neighbours. Advances in Mathematics of Communications,
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