New Type I Binary [72, 36, 12] Self-Dual Codes from Composite Matrices and R1 Lifts

2021/01/31 by Korban, Adrian, Sahinkaya, Serap, Ustun, Deniz
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2102.00474

Abstract

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].

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