Repeated-root constacyclic codes of length 6<i>l^mpⁿ</i>

&lt;p style='text-indent:20px;'&gt;Let &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \mathbb{F}_{q} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; be a finite field with character id="M2"&gt;\begin{document}$ p $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. In this paper, the multiplicative group id="M3"&gt;\begin{document}$ \mathbb{F}_{q}^{*} = \mathbb{F}_{q}\setminus\{0\} is decomposed into mutually disjoint union of id="M4"&gt;\begin{document}$ \gcd(6l^mp^n,q-1) cosets over subgroup id="M5"&gt;\begin{document}$ &amp;lt;\xi^{6l^mp^n}&amp;gt; $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, where id="M6"&gt;\begin{document}$ \xi primitive element id="M7"&gt;\begin{document}$ Based on decomposition, structure constacyclic codes length id="M8"&gt;\begin{document}$ 6l^mp^n id="M9"&gt;\begin{document}$ and their duals established in terms generator polynomials, id="M10"&gt;\begin{document}$ p\neq{3} id="M11"&gt;\begin{document}$ l\neq{3} are distinct odd primes, id="M12"&gt;\begin{document}$ m id="M13"&gt;\begin{document}$ n positive integers. addition, we determine characterization enumeration all linear complementary dual(LCD) negacyclic self-dual id="M14"&gt;\begin{document}$ id="M15"&gt;\begin{document}$ $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;.&lt;/p&gt;