Cross-correlation coefficients for digit sequences of uniform linear recurrent sequences over the residue ring

We study the class of sequences over the prime field with $p$ elements formed by the most significant $p$-ary digits of linear recurrent sequences over the residue ring modulo $p^n$. We obtain absolute and nonabsolute bounds for the cross-correlation coefficients of such sequences. This results lead to some sufficient conditions for segments of digit sequences obtained from different initial sequences to be different.