Properties of cross-correlation between two P-ary m-sequences of different periods

Recently,Ness and Helleseth initiated studies on the cross-correlation between two binary m-sequences of different periods.Based on their results,we analyse the properties of the cross-correlation between two p-ary m-sequences of different periods,and give the equations for the cross-correlation values to be met.Finally,for p=3,it is proved that the cross-correlation values takes on at least three different values.