Repeated-root bidimensional \((\mu, \nu)\)-constacyclic codes of length \(4p^t.2^r\) (Q2024768)

Summary: Let \(p\) be an odd prime. The main concern of this article is to study all the repeated-root bidimensional \((\mu, \nu)\)-constacyclic codes of length \(4p^t.2^r\) over the finite field \(\mathbb{F}_{ p^m} \). Here, we provide all the self-dual repeated-root bidimensional (1, 1)-constacyclic and \((-1, 1)\)-constacyclic codes of length \(4p^t.2^r\) over \(\mathbb{F}_{ p^m} \). We also discuss the repeated-root bidimensional \((\eta, 1)\)-constacyclic codes of length \(4p^t.2^r\) over \(\mathbb{F}_{ p^m} \). Moreover, it has been shown that these structures are useful in the construction of linear complementary dual (\textit{LCD}) codes and self-dual codes. As an example, we are listed all the repeated-root bidimensional \((\mu, \nu)\)-constacyclic codes of length 72 over the finite field \(\mathbb{F}_{27} \).