LCD Codes and Self-orthogonal Codes in Finite Dihedral Group Algebras

Abstract

Let ${\mathbb{F}_q}$ be a finite field with order q and D _2n be the dihedral group with 2n elements, and gcd(q, 2n) = 1. In this article, the authors give precise descriptions and enumerations of linear complementary dual (LCD) codes and self-orthogonal codes in the finite dihedral group algebras ${\mathbb{F}_q}[{D_{2n}}]$. Some numerical examples are also presented to illustrate the main results.

Keywords

Group algebra / Dihedral group / LCD codes / Self-orthogonal codes