Bordered Constructions of Self-Dual Codes from Group Rings and New Extremal Binary Self-Dual Codes
AffiliationUniversity of Scranton; University of Chester; Sampoerna Academy; Uzhgorod State University; Northern Arizona University
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AbstractWe 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.
CitationDougherty, 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
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