A family of constacyclic codes over \(\mathbb{F}_{ p^m} [\upsilon, w]/\langle \upsilon^2 - 1, w^2 - 1, \upsilon w - w \upsilon \rangle \) (Q2024756)

Summary: In this article, for any odd prime \(p\), we study the constacyclic and skew constacyclic codes of arbitrary length over \(R = \mathbb{F}_{ p^m} [\upsilon, w]/\langle \upsilon^2 - 1, w^2 - 1, \upsilon w - w \upsilon \rangle \). It is shown that the Gray images of constacyclic and skew constacyclic codes of length \(n\) over \(R\) are quasi-twisted and skew quasi-twisted codes, respectively over \(\mathbb{F}_{ p^m}\) of length \(4 n\) with index 4. Also, the structures of constacyclic and skew constacyclic codes are obtained by decomposition method.