Distribution Properties of Compressing Sequences Derived From Primitive Sequences Modulo Odd Prime Powers

摘要

Let (underline {a}) and (underline {b}) be primitive sequences over (mathbb {Z}/(p^{e})) with odd prime (p) and (ege 2) . For certain compressing maps, we consider the distribution properties of compressing sequences of (underline {a}) and (underline {b}) , and prove that (underline {a}=underline {b}) if the compressing sequences are equal at the times (t) such that (alpha (t)=k) , where (underline {alpha }) is a sequence related to (underline {a}) . We also discuss the (s) -uniform distribution property of compressing sequences. For some compressing maps, we obtain that there exist different primitive sequences such that the compressing sequences are (s) -uniform. We also discuss that for how many elements (s) , compressing sequences of different primitive sequences can be (s) -uniform.