Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme
AffiliationUniversity of Scranton; University of Chester; Tarsus University
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AbstractWe present a generator matrix of the form [ \sigma(v_1) \ | \ \sigma(v_2)] where v_1 \in RG and v_2\in RH for finite groups G and H of order n for constructing self-dual codes and linear complementary dual codes over the finite Frobenius ring R. In general, many of the constructions to produce self-dual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find self-dual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve 10 of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain 82 new binary linear complementary dual codes 50 of which are either optimal or near optimal of lengths 41 \leq n \leq 61 which are new to the literature.
CitationDougherty, S., Korban, A., Şahinkaya, S., & Ustun, D. (2022). Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme. Advances in Mathematics of Communications, vol(issue), pages. https://doi.org/10.3934/amc.2022036
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