The combinatorics of LCD codes: linear programming bound and orthogonal matrices. (2017)

• Record Type: Journal Article
• Authors: Dougherty, Steven T.; Kim, Jon-Lark; Ozkaya, Buket; Sok, Lin; Solé, Patrick
• Is Part Of: International journal of information and coding theory. Volume 4:Number 2/3(2017)
• Page Start: 116
• Page End: 128
• Publication Date: 2017
• Subjects: LCD (linear codes with complementary dual) codes -- linear programming bound -- self-dual codes; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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.