The combinatorics of LCD codes: linear programming bound and orthogonal matrices Online publication date: Mon, 24-Apr-2017
by Steven T. Dougherty; Jon-Lark Kim; Buket Ozkaya; Lin Sok; Patrick Solé
International Journal of Information and Coding Theory (IJICOT), Vol. 4, No. 2/3, 2017
Abstract: Linear complementary dual (LCD) codes 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 Rk. 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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