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

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dc.authoridhttps://orcid.org/0000-0002-2084-6260en_US
dc.authoridhttps://orcid.org/0000-0002-5229-4018en_US
dc.authorscopusid36728602600en_US
dc.authorscopusid55420759300en_US
dc.authorscopusid57206665622en_US
dc.authorwosidDWJ-0396-2022en_US
dc.authorwosidABB-4228-2020en_US
dc.authorwosidG-2829-2015en_US
dc.contributor.authorKorban, Adrian
dc.contributor.authorÜstün, Deniz
dc.contributor.authorŞahinkaya, Serap
dc.date.accessioned2024-08-01T13:52:37Z
dc.date.available2024-08-01T13:52:37Z
dc.date.issued2021en_US
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümüen_US
dc.description.abstractIn 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.citationKorban, 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.doi10.48550/arXiv.2109.06522en_US
dc.identifier.urihttps://doi.org/10.48550/arXiv.2109.06522 Focus to learn more
dc.identifier.urihttps://hdl.handle.net/20.500.13099/317
dc.institutionauthorŞahinkaya, Serap
dc.institutionauthorÜstün, Deniz
dc.language.isoengen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectself-dual codesen_US
dc.subjectlinear codesen_US
dc.subjectneighbour methoden_US
dc.subjectvirus optimization algorithmen_US
dc.titleNew 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 Algorithmen_US
dc.typearticleen_US

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