Z(p/sup k+1/)-linear codes

Abstract

We characterize codes over Z/sub p/ which are the Gray images of (1-p/sup k/)-cyclic codes or cyclic codes over Z(p/sup k+l/) (k/spl ges/1). A necessary and sufficient condition for the Gray image of a Z(p/sup 2/)-linear (1-p)-cyclic code to be linear is given. In many cases, this yields an explicit description of the Gray image of a linear (1-p)-cyclic code over Z(p/sup 2/), of length relatively prime to p. Linear cyclic codes over Z(p/sup 2/) whose Gray images are linear cyclic codes over Z/sub p/ have been characterized. Some generalizations of these results to the case of Z(p/sup k+1/), where k/spl ges/2, are also obtained.