On some constacyclic codes over the ring Fpm[u]∕〈u4〉

Let R be the finite chain ring R=Fpm[u]∕〈u4〉, where p is a prime and m is a positive integer. In this work, we give a complete classification of (1+αu2)-constacyclic codes of length pk over R, where α is a nonzero element of Fpm. We also completely determine self-dual such codes and enumerate them. Finally we discuss on Gray-maps on R which preserve self-duality, and also discuss on the images of self-dual constacyclic codes under these Gray maps.