Upper Bound on the Cross-Correlation between Two Decimated Sequences

In this paper, for an odd prime p, two positive integers n, m with n=2m, and pm≡1 (mod 4), we derive an upper bound on the magnitude of the cross-correlation function between two decimated sequences of a p-ary m-sequence. The two decimation factors are 2 and 2(pm+1), and the upper bound is derived as $\frac{3}{2}p^m + \frac{1}{2}$. In fact, those two sequences correspond to the p-ary sequences used for the construction of Kasami sequences decimated by 2. This result is also used to obtain an upper bound on the cross-correlation magnitude between a p-ary m-sequence and its decimated sequence with the decimation factor $d=\frac{(p^m +1)^2}{2}$.