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Advances in Mathematics of Communications (AMC)
 

The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$

Pages: 409 - 424, Volume 7, Issue 4, November 2013      doi:10.3934/amc.2013.7.409

 
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Yuhua Sun - College of Sciences, China University of Petroleum, 66 Changjiang Xilu, Qingdao, Shandong 266580, China (email)
Zilong Wang - State Key Laboratory of Integrated Service Networks, Xidian University, 2 Taibai Nanlu, Xi'an, Shannxi 710071, China (email)
Hui Li - State Key Laboratory of Integrated Service Networks, Xidian University, 2 Taibai Nanlu, Xi'an, Shannxi 710071, China (email)
Tongjiang Yan - 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 $p^n-1$ and its decimated sequence $\{s_{dt}\}$, where $d=\frac{(p^k+1)^2}{2(p^e+1)}$, $e|k$ and $n = 2k$. Using quadratic form polynomial theory, we obtain the distribution of the cross correlation which is six-valued. 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, p-ary m-sequence, quadratic form.
Mathematics Subject Classification:  Primary: 94A55; Secondary: 11B50.

Received: May 2012;      Available Online: October 2013.

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