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arXiv · 2002.10030

New Extremal binary self-dual codes of length 68 from a novel approach to neighbors

Joe Gildea·Abidin Kaya·Adrian Korban·Bahattin Yildiz
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Abstract

In this work, we introduce the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the k-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight enumerators. We construct 143 extremal binary self-dual codes of length 68 with new weight enumerators including 42 codes with gamma=8 in their W_{68,2} and 40 with gamma=9 in their W_{68,2}. These examples are the first in the literature for these gamma values. This completes the theoretical list of possible values for gamma in W_{68,2}.

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Joe Gildea, Abidin Kaya, Adrian Korban, Bahattin Yildiz. 2020-02-24. New Extremal binary self-dual codes of length 68 from a novel approach to neighbors. https://arxiv.org/abs/2002.10030

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