Composite matrices from group rings, composite G -codes and constructions of self-dual codes
AuthorsDougherty, Steven T.
Korban, Adrian; orcid: 0000-0001-5206-6480; email: firstname.lastname@example.org
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AbstractAbstract: In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a composite G-code is also a composite G-code. We also define quasi-composite G-codes. Additionally, we study generator matrices, which consist of the identity matrices and the composite matrices. Together with the generator matrices, the well known extension method, the neighbour method and its generalization, we find extremal binary self-dual codes of length 68 with new weight enumerators for the rare parameters γ=7, 8 and 9. In particular, we find 49 new such codes. Moreover, we show that the codes we find are inaccessible from other construction
CitationDesigns, Codes and Cryptography, volume 89, issue 7, page 1615-1638
DescriptionFrom Springer Nature via Jisc Publications Router
History: received 2020-02-25, rev-recd 2021-02-09, accepted 2021-04-17, registration 2021-04-17, pub-electronic 2021-05-19, online 2021-05-19, pub-print 2021-07
Publication status: Published
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