A class of constacyclic codes over and its Gray image

We introduce a Gray map from F p + v F p to F p 2 and study ( 1 − 2 v ) -constacyclic codes over F p + v F p , where v 2 = v . It is proved that the image of a ( 1 − 2 v ) -constacyclic code of length n over F p + v F p under the Gray map is a distance-invariant linear cyclic code of length 2 n over F p . The generators of such constacyclic codes for an arbitrary length are determined and their dual codes are also discussed.