Korban, AdrianŞahinkaya, SerapÜstün, Deniz2024-08-012024-08-012022Dougherty, S.T., Korban, A., Sahinkaya, S. ve Ustun, D. (2022). New type I binary [72,36, 12] self-dual codes from M6(F2) G-Group matrix rings by a hybrid search technique based on a neighbourhood-virus optimisation algorithm. Advances in Mathematics of Communications, 18 (4), 878-891.1930-53461930-5338https://www.aimsciences.org/article/doi/10.3934/amc.2022032?viewType=htmlhttps://hdl.handle.net/20.500.13099/310In this paper, a new search technique based on a virus optimisation algorithm is proposed for calculating the neighbours of binary self-dual codes. The aim of this new technique is to calculate neighbours of self-dual codes without reducing the search field in the search process (this technique is known in the literature due to the computational time constraint) but still obtaining results in a reasonable time (significantly faster when compared to the standard linear computational search). We employ this new search algorithm to the well-known neighbour method and its extension, the kth -range neighbours, and search for binary [72, 36, 12] self-dual codes. In particular, we present six generator matrices of the form [I-36 vertical bar tau(6) (v)], where I-36 is the 36 x 36 identity matrix, v is an element in the group matrix ring M-6(F-2)G and G is a finite group of order 6, to which we employ the proposed algorithm and search for binary [72, 36, 12] self-dual codes directly over the finite field F-2. We construct 1471 new Type I binary [72,36,12] self-dual codes with the rare parameters gamma = 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32 in their weight enumerators.eninfo:eu-repo/semantics/restrictedAccessLinear codesbinary self-dual codesgroup matrix ringsneighbours of self-dual codesevolutionary algorithmsArticle10.3934/amc.2022032184878891Q3WOS:0007930783000012-s2.0-85196812113Q1