Constacyclic codes of arbitrary lengths over ring Z_{p^m } + vZ_{p^m }

By constructing a Gray map, constacyclic codes of arbitrary lengths over ring \(R = Z_{p^m } + vZ_{p^m }\) are studied, where v ² = v The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular, (1+(v+1)αp)-constacyclic codes over R are classified in terms of generator polynomial, where α is a unit of \(Z_{p^m }\) .