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Group matrix ring codes and constructions of self-dual codes
Dougherty, Steven T. Korban, Adrian Şahinkaya, Serap Ustun, Deniz
Dougherty, Steven T.
Korban, Adrian
Şahinkaya, Serap
Ustun, Deniz
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2021-04-02
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Abstract
In 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.
Citation
Dougherty, S. T., Korban, A., Şahinkaya, S., & Ustun, D. (2023). Group matrix ring codes and constructions of self-dual codes. Applicable Algebra in Engineering, Communication and Computing, 34, 279–299. https://doi.org/10.1007/s00200-021-00504-9
Publisher
Springer
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Applicable Algebra in Engineering, Communication and Computing
Research Unit
DOI
10.1007/s00200-021-00504-9
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Article
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The version of record of this article, first published in [Applicable Algebra in Engineering, Communication and Computing], is available online at Publisher’s website: http://dx.doi.org/10.1007/s00200-021-00504-9
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ISSN
0938-1279