Binary linear complementary dual codes

Abstract

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary linear complementary dual $[n,k]$ codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete classification of binary linear complementary dual $[n,k]$ codes with the largest minimum weight is also given for $1 \le k \le n \le 16$.