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
dc.authorid | https://orcid.org/0000-0002-2084-6260 | en_US |
dc.authorid | https://orcid.org/0000-0002-5229-4018 | en_US |
dc.authorscopusid | 36728602600 | en_US |
dc.authorscopusid | 55420759300 | en_US |
dc.authorscopusid | 57206665622 | en_US |
dc.authorwosid | DWJ-0396-2022 | en_US |
dc.authorwosid | ABB-4228-2020 | en_US |
dc.authorwosid | G-2829-2015 | en_US |
dc.contributor.author | Korban, Adrian | |
dc.contributor.author | Üstün, Deniz | |
dc.contributor.author | Şahinkaya, Serap | |
dc.date.accessioned | 2024-08-01T13:52:37Z | |
dc.date.available | 2024-08-01T13:52:37Z | |
dc.date.issued | 2021 | en_US |
dc.department | Fakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü | en_US |
dc.description.abstract | In 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. | en_US |
dc.identifier.citation | Korban, 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). | en_US |
dc.identifier.doi | 10.48550/arXiv.2109.06522 | en_US |
dc.identifier.uri | https://doi.org/10.48550/arXiv.2109.06522 Focus to learn more | |
dc.identifier.uri | https://hdl.handle.net/20.500.13099/317 | |
dc.institutionauthor | Şahinkaya, Serap | |
dc.institutionauthor | Üstün, Deniz | |
dc.language.iso | eng | en_US |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | self-dual codes | en_US |
dc.subject | linear codes | en_US |
dc.subject | neighbour method | en_US |
dc.subject | virus optimization algorithm | en_US |
dc.title | 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 | en_US |
dc.type | article | en_US |