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/0000-0002-2084-6260en_US
dc.authoridhttps://orcid.org/0000-0002-5229-4018en_US
dc.authorscopusid26325279300en_US
dc.authorscopusid57206665622en_US
dc.authorscopusid55420759300en_US
dc.authorscopusid36728602600en_US
dc.authorwosidGQB-3301-2022en_US
dc.authorwosidABB-4228-2020en_US
dc.authorwosidIDO-2426-2023en_US
dc.authorwosidDWJ-0396-2022en_US
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.issued2022en_US
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümüen_US
dc.description.abstractWe present a generator matrix of the form [σ(v1) | σ(v2)], where v1 ϵ RG and v2 ϵ 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.en_US
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.en_US
dc.identifier.doi10.3934/amc.2022036en_US
dc.identifier.endpage934en_US
dc.identifier.issn1930-5346
dc.identifier.issn1930-5338
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85196910543en_US
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.wos000807233100001en_US
dc.identifier.wosqualityQ3en_US
dc.institutionauthorÜstün, Deniz
dc.institutionauthorŞahinkaya, Serap
dc.language.isoengen_US
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en_US
dc.relation.ispartofAdvances in Mathematics of Communicationsen_US
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/restrictedAccessen_US
dc.subjectLCD codesen_US
dc.subjectself-dual codesen_US
dc.subjectG-codesen_US
dc.subjectbinary codesen_US
dc.subjectheuristic algoritmen_US
dc.titleBinary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search schemeen_US
dc.typearticleen_US

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