Enumeration of complementary-dual cyclic ${\mathbb{F}}_q$-linear ${\mathbb{F}}_{q^t}$-codes

Abstract

Let ${\mathbb{F}}_q$ denote the finite field of order $q,$ $n$ be a positive integer coprime to $q$ and $t\ge 2$ be an integer. In this paper, we enumerate all the complementary-dual cyclic ${\mathbb{F}}_q$-linear ${\mathbb{F}}_{q^t}$-codes of length $n$ by placing $\ast$, ordinary and Hermitian trace bilinear forms on ${\mathbb{F}}_{q^t}^n.$

This work is a part of PhD thesis of Ms. Taranjot Kaur