Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme

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dc.authoridhttps://orcid.org/0000-0002-2084-6260
dc.authoridhttps://orcid.org/0000-0002-5229-4018
dc.authorscopusid26325279300
dc.authorscopusid57206665622
dc.authorscopusid55420759300
dc.authorscopusid36728602600
dc.authorwosidGQB-3301-2022
dc.authorwosidABB-4228-2020
dc.authorwosidIDO-2426-2023
dc.authorwosidDWJ-0396-2022
dc.contributor.authorDougherty, S. T.
dc.contributor.authorKorban, Adrian
dc.contributor.authorŞahinkaya, Serap
dc.contributor.authorÜstün, Deniz
dc.date.accessioned2024-07-31T14:20:04Z
dc.date.available2024-07-31T14:20:04Z
dc.date.issued2022
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
dc.description.abstractWe present a generator matrix of the form [?(v1) | ?(v2)], where v1 ? RG and v2 ? 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 ? n ? 61 which are new to the literature.
dc.identifier.citationDougherty, S., Korban, A., Sahinkaya, 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, 18(4), 922-934.
dc.identifier.doi10.3934/amc.2022036
dc.identifier.endpage934en_US
dc.identifier.issn1930-5346
dc.identifier.issn1930-5338
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85196910543
dc.identifier.scopusqualityQ1
dc.identifier.startpage922en_US
dc.identifier.urihttps://www.aimsciences.org/article/doi/10.3934/amc.2022036?viewType=html
dc.identifier.urihttps://hdl.handle.net/20.500.13099/309
dc.identifier.volume18en_US
dc.identifier.wosWOS:000807233100001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÜstün, Deniz
dc.institutionauthorŞahinkaya, Serap
dc.language.isoen
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.ispartofAdvances in Mathematics of Communications
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/restrictedAccess
dc.subjectLCD codes
dc.subjectself-dual codes
dc.subjectG-codes
dc.subjectbinary codes
dc.subjectheuristic algoritm
dc.titleBinary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme
dc.typeArticle

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