On (α + u β) constacyclic codes of length 4ps over Fpm + uFpm

Abstract

© 2019 World Scientific Publishing Company. For any odd prime p such that pm ≡ 3(mod 4), the structures of all (α+uβ)-constacyclic codes of length 4ps over the finite commutative chain ring pm + upm (u2 = 0) are established in term of their generator polynomials. When the unit (α + uβ) is a square, each (α + uβ)-constacyclic code of length 4ps is expressed as a direct sum of two constacyclic codes of length 2ps. In the main case that the unit (α + uβ) is not a square, it is shown that the ambient ring (pm+upm)[x] (x4ps-(α+uβ)) is a principal ideal ring. From that, the structure, number of codewords, duals of all such (α + uβ)-constacyclic codes are obtained. As an application, we identify all self-orthogonal, dual-containing, and the unique self-dual (α + uβ)-constacyclic codes of length 4ps over pm + upm.