The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices
Information Theory
2015-06-08 v1 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 . 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.
Cite
@article{arxiv.1506.01955,
title = {The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices},
author = {Steven T. Dougherty and Jon-Lark Kim and Buket Ozkaya and Lin Sok and Patrick Solé},
journal= {arXiv preprint arXiv:1506.01955},
year = {2015}
}
Comments
submitted to Linear Algebra and Applications on June, 1, 2015