Additive complementary dual codes from group characters

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dc.authoridhttps://orcid.org/0000-0002-5229-4018
dc.authoridhttps://orcid.org/0000-0002-2084-6260
dc.authorscopusid26325279300
dc.authorscopusid55420759300
dc.authorscopusid36728602600
dc.authorwosidCOV-5724-2022
dc.authorwosidABB-4228-2020
dc.authorwosidGQB-3301-2022
dc.contributor.authorDougherty, S. T.
dc.contributor.authorŞahinkaya, Serap
dc.contributor.authorÜstün, Deniz
dc.date.accessioned2024-08-01T12:35:36Z
dc.date.available2024-08-01T12:35:36Z
dc.date.issued2022
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
dc.description.abstractAdditive codes have become an increasingly important topic in algebraic coding theory due to their applications in quantum error-correction and quantum computing. Linear Complementary Dual (LCD) codes play an important role for improving the security of information against certain attacks. Motivated by these facts, we define additive complementary dual codes (ACD for short) over a finite abelian group in terms of an arbitrary duality on the ambient space and examine their properties. We show that the best minimum weight of ACD codes is always greater than or equal to the best minimum weight of LCD codes of the same size and that this inequality is often strict. We give some matrix constructions for quaternary ACD codes from a given quaternary ACD code and also from a given binary self-orthogonal code. Moreover, we construct an algorithm to determine if a given quaternary additive code is an ACD code with respect to all possible symmetric dualities. We also determine the largest minimum distance of quaternary ACD codes for lengths n <= 10. The obtained codes are either optimal or near optimal according to Bierbrauer et al+. (2009).
dc.identifier.citationDougherty, S. T., Şahinkaya, S. ve Üstün, D. (2022). Additive Complementary Dual Codes From Group Characters, IEEE Transactions on Information Theory, 68 (7), 4444-4452. Doi: 10.1109/TIT.2022.3162181
dc.identifier.doi10.1109/TIT.2022.3162181
dc.identifier.endpage4452en_US
dc.identifier.issn0018-9448
dc.identifier.issn1557-9654
dc.identifier.issue7en_US
dc.identifier.scopus2-s2.0-85132232811
dc.identifier.scopusqualityQ1
dc.identifier.startpage4444en_US
dc.identifier.urihttps://ieeexplore.ieee.org/abstract/document/9741715
dc.identifier.urihttps://hdl.handle.net/20.500.13099/314
dc.identifier.volume68en_US
dc.identifier.wosWOS:000812529200023
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÜstün, Deniz
dc.institutionauthorŞahinkaya, Serap
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.ispartofIEEE Transactions on Information Theory
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/restrictedAccess
dc.subjectLCD codes
dc.subjectadditive codes
dc.subjectoptimal codes
dc.titleAdditive complementary dual codes from group characters
dc.typeArticle

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