Dougherty, Steven T.Korban, AdrianŞahinkaya, SerapUstun, Deniz2023-02-212023-02-212021-04-02Dougherty, 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/s00200-021-00504-90938-127910.1007/s00200-021-00504-9http://hdl.handle.net/10034/627578The 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/s00200-021-00504-9In 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.Licence for this article: http://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/Original PaperGroup Matrix RingsLinear CodesSelf-Dual CodesCodes over RingsArticleApplicable Algebra in Engineering, Communication and Computing2023-02-21