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

## TL;DR

This paper systematically enumerates all complementary-dual cyclic codes over finite fields, considering various trace bilinear forms, providing a comprehensive classification relevant for coding theory applications.

## Contribution

It introduces a complete enumeration method for complementary-dual cyclic codes over finite fields using different trace bilinear forms.

## Key findings

- Enumeration formulas for all such codes
- Classification based on trace bilinear forms
- Explicit counts for specific parameters

## Abstract

Let $\mathbb{F}_q$ denote the finite field of order $q,$ $n$ be a positive integer coprime to $q$ and $t \geq 2$ 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 $\mathbb{F}_{q^t}^n.$