[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]-linear codes

We characterize codes over [Z.sub.p] which are the Gray images of (1 - [p.sup.k])-cyclic codes or cyclic codes over [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (k [greater than or equal to] 1). A necessary and sufficient condition for the Gray image of a [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]-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 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], of length relatively prime to p. Linear cyclic codes over [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] a whose Gray images are linear cyclic codes over [Z.sub.p] have been characterized. Some generalizations of these results to the case of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where k [greater than or equal to] 2, are also obtained. Index Terms--Constacyclic code, cyclic code, Gray map, linear code, quasi-cyclic code.