The crosscorrelation 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  College of Sciences, China University of Petroleum, 66 Changjiang Xilu, Qingdao, Shandong 266580, China (email) Abstract: Families of $m$sequences with low correlation property have important applications in communication systems. In this paper, for a prime $p\equiv 1\ \mathrm{mod}\ 4$ and an odd integer $k$, we study the cross correlation between a $p$ary $m$sequence $\{s_t\}$ of period $p^n1$ and its decimated sequence $\{s_{dt}\}$, where $d=\frac{(p^k+1)^2}{2(p^e+1)}$, $ek$ and $n = 2k$. Using quadratic form polynomial theory, we obtain the distribution of the cross correlation which is sixvalued. Specially, our results show that the magnitude of the cross correlation is upper bounded by $2\sqrt{p^n}+1$ for $p=5$ and $e=1$, which is meaningful in CDMA communication systems.
Keywords: Cross correlation, decimated sequence, pary msequence, quadratic
form.
Received: May 2012; Available Online: October 2013. 
2016 Impact Factor.8
