The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$
Yuhua Sun, Zilong Wang, Hui Li, Tongjiang Yan · Advances in Mathematics of Communications · 2013
Families of $m-$sequences with low correlation property haveimportant applications in communication systems. In this paper, fora prime $p\equiv 1\ \mathrm{mod}\ 4$ and an odd integer $k$, we studythe cross correlation between a $p$-ary $m$-sequence $\{s_t\}$ ofperiod $p^n-1$ and its decimated sequence $\{s_{dt}\}$, where$d=\frac{(p^k+1)^2}{2(p^e+1)}$, $e|k$ and $n = 2k$. Usingquadratic form polynomial theory, we obtain the distributionof the cross correlation which is six-valued. Specially, our results show that the magnitude of the cross correlation is upperbounded by $2\sqrt{p^n}+1$ for$p=5$ and $e=1$, which is meaningful in CDMAcommunication systems.