Zpk+1-linear codes
We characterize codes over Z(p) which are the Gray images of (1 - p(k))-cyclic codes or cyclic codes over Z(pk+1) (k greater than or equal to 1). A necessary and sufficient condition for the Gray image of a Z(p2)-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(p2), of length relatively prime to p. Linear cyclic codes over Z(p2) whose Gray images are linear cyclic codes over Z(p) have been characterized. Some generalizations of these results to the case of Z(pk+1), where k greater than or equal to 2, are also obtained.
cyclic code constacyclic code gray map linear code quasi-cyclic code