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

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.

preprint2015arXivOpen access
Steven T. DoughertyJon-Lark KimBuket OzkayaLin SokPatrick Solé
math.ITInformation Theory
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Steven T. DoughertyJon-Lark KimBuket OzkayaLin SokPatrick Solé

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