# Construction of Isodual Quasi-cyclic Codes over Finite Fields

## TL;DR

This paper investigates the conditions for constructing isodual quasi-cyclic codes over finite fields, establishing equivalence criteria and proposing new construction methods including matrix product approaches.

## Contribution

It provides new theoretical conditions for the existence of isodual quasi-cyclic codes and introduces a matrix product construction method.

## Key findings

- Permutation equivalence of quasi-cyclic codes characterized
- Conditions for the existence of isodual quasi-cyclic codes established
- A new construction method using matrix products proposed

## Abstract

This paper considers the construction of isodual quasi-cyclic codes. First we prove that two quasi-cyclic codes are permutation equivalent if and only if their constituent codes are equivalent. This gives conditions on the existence of isodual quasi-cyclic codes. Then these conditions are used to obtain isodual quasi-cyclic codes. We also provide a construction for isodual quasi-cyclic codes as the matrix product of isodual codes.