Affiliation
University of Scranton; University of Chester; Tarsus UniversityPublication Date
2021-04-02
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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, pages279–299. https://doi.org/10.1007/s00200-021-00504-9Publisher
SpringerAdditional Links
https://link.springer.com/article/10.1007/s00200-021-00504-9Type
ArticleDescription
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/s00200-021-00504-9ISSN
0938-1279ae974a485f413a2113503eed53cd6c53
10.1007/s00200-021-00504-9
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Except where otherwise noted, this item's license is described as Licence for this article: http://creativecommons.org/licenses/by/4.0/