Some Results on Cross-Correlation Distribution Between a \(p\) -Ary \(m\) -Sequence and Its Decimated Sequences.

For an odd prime \(p\) and two positive integers \(m\) , \(k\) such that \(m/\gcd (k,m)\geq 3\) is odd, let \(d\) be a positive integer satisfying \(d(p^{k}+1)\equiv 2\,({\rm mod}\,p^{m}-1)\) . 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. [ABSTRACT FROM PUBLISHER]