On constacyclic codes over finite fields

Constacyclic codes are generalizations of cyclic codes, which form a well-known family of linear codes containing many optimal codes. In this paper, we determine all constacyclic codes of length ℓpw over the finite field 𝔽q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {F}_{q}$\end{document} with q elements, where q is a power of the prime p, ℓ is a positive integer coprime to q and w ≥ 0 is an integer. We also illustrate our results with some examples.