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On $ \mathbb{Z}_4\mathbb{Z}_4[u^3] $-additive constacyclic codes
Advances in Mathematics of Communications ( IF 0.9 ) Pub Date : 2022-01-01 , DOI: 10.3934/amc.2022017 Om Prakash 1 , Shikha Yadav 1 , Habibul Islam 1 , Patrick Solé 2
Advances in Mathematics of Communications ( IF 0.9 ) Pub Date : 2022-01-01 , DOI: 10.3934/amc.2022017 Om Prakash 1 , Shikha Yadav 1 , Habibul Islam 1 , Patrick Solé 2
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<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Z}_4 $\end{document}</tex-math></inline-formula> be the ring of integers modulo <inline-formula><tex-math id="M3">\begin{document}$ 4 $\end{document}</tex-math></inline-formula>. This paper studies mixed alphabets <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{Z}_4\mathbb{Z}_4[u^3] $\end{document}</tex-math></inline-formula>-additive cyclic and <inline-formula><tex-math id="M5">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-constacyclic codes for units <inline-formula><tex-math id="M6">\begin{document}$ \lambda = 1+2u^2,3+2u^2 $\end{document}</tex-math></inline-formula>. First, we obtain the generator polynomials and minimal generating set of additive cyclic codes. Then we extend our study to determine the structure of additive constacyclic codes. Further, we define some Gray maps and obtain <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{Z}_4 $\end{document}</tex-math></inline-formula>-images of such codes. Finally, we present numerical examples that include six new and two best-known quaternary linear codes.</p>
更新日期：2022-01-01
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