A class of constacyclic codes containing formally self-dual and isodual codes

Abstract

In this paper, we investigate a class of constacyclic codes which contains isodual codes and formally self-dual codes. Further, we introduce a recursive approach to obtain the explicit factorization of $x^{2^m\ell^n}-\mu_k\in\mathbb{F}_q[x]$, where $n, m$ are positive integers and $\mu_k$ is an element of order $\ell^k$ in $\mathbb{F}_q$. Moreover, we give many examples of interesting isodual and formally self-dual constacyclic codes.