Emergent Mind
The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices
(1506.01955)
Published Jun 5, 2015
in
cs.IT
and
math.IT
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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