New Type I Binary [72,36,12] Self-Dual Codes From Composite Matrices And R-1 Lifts
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CitationKorban, A. Sahinkaya, Serap ve Ustun, D. (2023). New Type I Binary [72,36,12] Self-Dual Codes From Composite Matrices And R-1 Lifts. Advances in Mathematics of Communications, 17 (4), 994 - 1011.
In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form [In | Ω(v)], where In is the identity matrix and Ω(v) is a composite matrix and search for binary self-dual codes with parameters [36, 18, 6 or 8]. We next lift these codes over the ring R1 = F2 + uF2 to obtain codes whose binary images are self-dual codes with parameters [72, 36, 12]. Many of these codes turn out to have weight enumerators with parameters that were not known in the literature before. In particular, we find 30 new Type I binary self-dual codes with parameters [72, 36, 12].