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AbstractIn this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring Mk(R) and the ring R, where R is the commutative Frobenius ring. We show that codes over the ring Mk(R) are one sided ideals in the group matrix ring Mk(R)G and the corresponding codes over the ring R are Gk-codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes.
CitationApplicable Algebra in Engineering, Communication and Computing, volume 34, issue 2, page 279-299
PublisherSpringer Berlin Heidelberg
DescriptionFrom Springer Nature via Jisc Publications Router
History: received 2021-01-30, rev-recd 2021-03-13, accepted 2021-03-19, registration 2021-03-20, pub-electronic 2021-04-02, online 2021-04-02, pub-print 2023-03
Publication status: Published