Title: The combinatorics of LCD codes: linear programming bound and orthogonal matrices

Authors: Steven T. Dougherty; Jon-Lark Kim; Buket Ozkaya; Lin Sok; Patrick Solé

Addresses: Department of Mathematics, University of Scranton, Scranton, PA 18510, USA ' Department of Mathematics, Sogang University, Seoul 04107, South Korea ' FENS, Sabancı University, 34956 İstanbul, Turkey ' Department of Mathematics, Anhui Hefei University, Hefei, PR China ' CNRS/LAGA, University of Paris 8, 93 526 Saint-Denis, France

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.

Keywords: LCD (linear codes with complementary dual) codes; linear programming bound; self-dual codes.

DOI: 10.1504/IJICOT.2017.083827

International Journal of Information and Coding Theory, 2017 Vol.4 No.2/3, pp.116 - 128

Received: 01 Aug 2016
Accepted: 26 Aug 2016

Published online: 20 Apr 2017 *

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