Upper Bound on the Cross-Correlation between Two Decimated Sequences

Chang-Min CHO  Wijik LEE  Jong-Seon NO  Young-Sik KIM  

IEICE TRANSACTIONS on Communications   Vol.E100-B   No.5   pp.837-842
Publication Date: 2017/05/01
Online ISSN: 1745-1345
DOI: 10.1587/transcom.2016EBP3182
Type of Manuscript: PAPER
Category: Wireless Communication Technologies
cross-correlation,  decimated sequences,  m-sequences,  p-ary sequences,  

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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 $ rac{3}{2}p^m + rac{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 $d= rac{(p^m +1)^2}{2}$.