On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers

Let Z/（p^e） be the integer residue ring modulo pewith p an odd prime and e 2. We consider the suniform property of compressing sequences derived from primitive sequences over Z/（p^e）. We give necessary and sufficient conditions for two compressing sequences to be s-uniform with α provided that the compressing map is of the form φ（x0, x1,..., xe-1） = g（xe-1） ＋ η（x0, x1,..., xe-2）, where g（xe-1） is a permutation polynomial over Z/（p） and η is an（e-1）-variable polynomial over Z/（p）.