On a class of constacyclic codes of length 4ps over 𝔽pm + u𝔽pm

Abstract

Let [Formula: see text] be a prime such that [Formula: see text]. For any unit [Formula: see text] of [Formula: see text], we determine the algebraic structures of [Formula: see text]-constacyclic codes of length [Formula: see text] over the finite commutative chain ring [Formula: see text], [Formula: see text]. If the unit [Formula: see text] is a square, 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] If the unit [Formula: see text] is not a square, then [Formula: see text] can be decomposed into a product of two irreducible coprime quadratic polynomials which are [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text]. By showing that the quotient rings [Formula: see text] and [Formula: see text] are local, non-chain rings, we can compute the number of codewords in each of [Formula: see text]-constacyclic codes. Moreover, the duals of such codes are also given.