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arXiv · 1506.01955

The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices

Steven T. Dougherty·Jon-Lark Kim·Buket Ozkaya·Lin Sok·Patrick Solé
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Abstract

Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$. We give a linear programming bound on the largest size of an LCD code of given length and minimum distance. We make a table of lower bounds for this combinatorial function for modest values of the parameters.

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Steven T. Dougherty, Jon-Lark Kim, Buket Ozkaya, Lin Sok, Patrick Solé. 2015-06-05. The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices. https://arxiv.org/abs/1506.01955

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