Cyclic and negacyclic codes of length 4ps over 𝔽pm + u𝔽pm

Abstract

Let [Formula: see text] be the finite field of order [Formula: see text] where [Formula: see text] is an odd prime and [Formula: see text] is a positive integer. In this paper, we determine the algebraic structures of all cyclic and negacyclic 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. We also obtain the number of codewords in each of these codes. Among others, we establish the duals of all such codes and derive some self-dual cyclic and negacyclic codes of length [Formula: see text] over [Formula: see text]