Korban, AdrianŞahinkaya, SerapÜstün, Deniz2024-08-012024-08-012021Korban, A., Şahinkaya, S. ve Üstün,D. (2021). New singly and doubly even binary [72,36,12] self-dual codes from M2(R)G - group matrix rings,Finite Fields and Their Applications,76. Erişim adresi: https://doi.org/10.1016/j.ffa.2021.101924.1071-57971090-2465https://www.sciencedirect.com/science/article/pii/S1071579721001180https://hdl.handle.net/20.500.13099/316In this work, we present a number of generator matrices of the form [I-2n vertical bar tau(2)(v)], where I-2n is the 2n x 2n identity matrix, v is an element in the group matrix ring M-2(R)G and where R is a finite commutative Frobenius ring and G is a finite group of order 18. We employ these generator matrices and search for binary [72, 36, 12] self-dual codes directly over the finite field F-2. As a result, we find 134 Type I and 1 Type II codes of this length, with parameters in their weight enumerators that were not known in the literature before. We tabulate all of our findings.enginfo:eu-repo/semantics/restrictedAccessGroup matrix ringsSelf-dual codesarticle10.1016/j.ffa.2021.10192476Q2000701889800023