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arXiv · 2102.00474

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

Adrian Korban·Serap Sahinkaya·Deniz Ustun
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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 | {\Omega}(v)], where In is the identity matrix and {\Omega}(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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Adrian Korban, Serap Sahinkaya, Deniz Ustun. 2021-01-31. New Type I Binary [72, 36, 12] Self-Dual Codes from Composite Matrices and R1 Lifts. https://arxiv.org/abs/2102.00474

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