Repeated-root constacyclic codes of length 6lmpn

Let \begin{document}$ \mathbb{F}_{q} $\end{document} be a finite field with character \begin{document}$ p $\end{document}. In this paper, the multiplicative group \begin{document}$ \mathbb{F}_{q}^{*} = \mathbb{F}_{q}\setminus\{0\} $\end{document} is decomposed into a mutually disjoint union of \begin{document}$ \gcd(6l^mp^n,q-1) $\end{document} cosets over subgroup \begin{document}$ <\xi^{6l^mp^n}> $\end{document}, where \begin{document}$ \xi $\end{document} is a primitive element of \begin{document}$ \mathbb{F}_{q} $\end{document}. Based on the decomposition, the structure of constacyclic codes of length \begin{document}$ 6l^mp^n $\end{document} over finite field \begin{document}$ \mathbb{F}_{q} $\end{document} and their duals is established in terms of their generator polynomials, where \begin{document}$ p\neq{3} $\end{document} and \begin{document}$ l\neq{3} $\end{document} are distinct odd primes, \begin{document}$ m $\end{document} and \begin{document}$ n $\end{document} are positive integers. In addition, we determine the characterization and enumeration of all linear complementary dual(LCD) negacyclic codes and self-dual constacyclic codes of length \begin{document}$ 6l^mp^n $\end{document} over \begin{document}$ \mathbb{F}_{q} $\end{document}.