Constructing Self-Dual Codes from Group Rings and Reverse Circulant Matrices
AffiliationUniversity of Chester; Sampoerna Academy; Northern Arizona University
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AbstractIn this work, we describe a construction for self-dual codes in which we employ group rings and reverse circulant matrices. By applying the construction directly over different alphabets, and by employing the well known extension and neighbor methods we were able to obtain extremal binary self-dual codes of different lengths of which some have parameters that were not known in the literature before. In particular, we constructed three new codes of length 64, twenty-two new codes of length 68, twelve new codes of length 80 and four new codes of length 92.
CitationGildea, J., Abidin, K., Adrian, K. & Bahattin, Y. (2020). Constructing self-dual codes from group rings and reverse circulant matrices. Advances in Mathematics of Communications, 15(3), 471-485. https://doi.org/10.3934/amc.2020077
DescriptionThis 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 Gildea, J., Abidin, K., Adrian, K. & Bahattin, Y. (2020). Constructing Self-Dual Codes from Group Rings and Reverse Circulant Matrices. Advances in Mathematics of Communications. is available online at: https://www.aimsciences.org/article/doi/10.3934/amc.2020077?viewType=html
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