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

  title={The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices},
  author={Steven T. Dougherty and Jon-Lark Kim and Buket {\"O}zkaya and Lin Sok and Patrick Sol{\'e}},
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 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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