Some Results on Cross-Correlation Distribution Between a <inline-formula> <tex-math notation="TeX">\(p\) </tex-math></inline-formula>-Ary <inline-formula> <tex-math notation="TeX">\(m\) </tex-math></inline-formula>-Sequence and Its Decimated Sequences

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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) .I n 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.