On the Construction of Some LCD Codes over Finite Fields

On the Construction of Some LCD Codes over Finite Fields

Abstract

Linear codes with complementary duals (LCD codes) are linear codes that intersect with their duals trivially. In this paper, we construct some families of LCD codes using Massey’s characterization of an LCD code. In particular, we obtain some classes of binary LCD codes using the permutation matrix and the all-one matrix. We also explicitly construct generator matrices of LCD codes using the generator matrices of self-dual codes and binary Hamming codes. For, 3 r 7 the binary LCD codes obtained using the Hamming matrix Hr are optimal.  We also consider some known methods of combining two or more codes such as the direct product, direct sum, and Plotkin sum. We show that the direct product and the direct sum of two LCD codes are also LCD. We also prove that the permutation equivalence of codes preserves the LCD-ness of linear codes.

On the Construction of Some LCD Codes over Finite Fields (723.1 KiB)