Some Results on Cross-Correlation Distribution Between a -Ary -Sequence and Its Decimated Sequences

For an odd prime p and two positive integers m, k such that m/gcd (k,m) ≥ 3 is odd, let d be a positive integer satisfying d(p^k+1)=2(mod p^m-1). In this paper, the cross-correlation between a p-ary m-sequence and its d-decimated sequences is investigated, and the cross correlation distribution is completely determined. The relationship between the decimations d considered in this paper and some known ones is also studied. This paper generalizes some previous results, and also gives new decimations, which lead to low cross correlation.