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arXiv · 1706.07631

New cubic self-dual codes of length 54, 60 and 66

Pınar Çomak·Jon-Lark Kim·Ferruh Özbudak
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Abstract

We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by constructing 1 new binary [54, 27, 10], 6 new [60, 30, 12] and 50 new [66, 33, 12] cubic self-dual codes. We conjecture that there exist no more binary cubic self-dual codes with length 54, 60 and 66.

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Pınar Çomak, Jon-Lark Kim, Ferruh Özbudak. 2017-06-23. New cubic self-dual codes of length 54, 60 and 66. https://arxiv.org/abs/1706.07631

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