Korban, AdrianÜstün, DenizŞahinkaya, Serap2024-08-012024-08-012021Korban, A., Şahinkaya, S. ve Üstün, D. (2021). New Extremal Binary Self-Dual Codes of Length 72 from M6(F2)G - Group Matrix Rings by a Hybrid Search Technique Based on a Neighbourhood-Virus Optimisation Algorithm, arXiv:2109.06522 (2021).https://doi.org/10.48550/arXiv.2109.06522 Focus to learn morehttps://hdl.handle.net/20.500.13099/317In this paper, a new search technique based on the 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 is a known in the literature approach 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 [I36 | τ6(v)], where I36 is the 36×36 identity matrix, v is an element in the group matrix ring M6(F2)G and G is a finite group of order 6, which we then employ to the proposed algorithm and search for binary [72,36,12] self-dual codes directly over the finite field F2. We construct 1471 new Type I binary [72,36,12] self-dual codes with the rare parameters γ=11,13,14,15,17,19,20,21,22,23,25,26,28,29,30,31,32 in their weight enumerators.enginfo:eu-repo/semantics/openAccessself-dual codeslinear codesneighbour methodvirus optimization algorithmarticle10.48550/arXiv.2109.06522