On a class of constacyclic codes of length 4ps over 𝔽pmu 〈u3〉

Let Formula: see text be a prime such that Formula: see text, where Formula: see text is a positive integer. For any nonzero element Formula: see text of Formula: see text, we determine the algebraic structure of all Formula: see text-constacyclic codes of length Formula: see text over the finite commutative chain ring Formula: see text, where Formula: see text and Formula: see text is a positive integer. If the unit Formula: see text is a square, Formula: see text, each Formula: see text-constacyclic code of length Formula: see text is expressed as a direct sum of an Formula: see text-constacyclic code and an Formula: see text- constacyclic code of length Formula: see text. In the main case that the unit Formula: see text is not a square, it is shown that any nonzero polynomial of degree at most Formula: see text over Formula: see text is invertible in the ambient ring Formula: see text. It is also proven that the ambient ring Formula: see text is a local ring with the unique maximal ideal Formula: see text, where Formula: see text. Such Formula: see text-constacyclic codes are then classified into eight distinct types of ideals, and the detailed structures of ideals in each type are provided. Among other results, the number of codewords, and the dual of each Formula: see text-constacyclic code are obtained. The non-existence of self-dual and isodual Formula: see text-constacyclic codes of length Formula: see text over Formula: see text, when the unit Formula: see text is not a square, is likewise proved.