On the Cross-Correlation between Two Decimated p-Ary m-Sequences by 2 and 4pn/2-2

Ji-Youp KIM  Chang-Min CHO  Wijik LEE  Jong-Seon NO  

IEICE TRANSACTIONS on Communications   Vol.E98-B   No.3   pp.415-421
Publication Date: 2015/03/01
Online ISSN: 1745-1345
DOI: 10.1587/transcom.E98.B.415
Type of Manuscript: PAPER
Category: Fundamental Theories for Communications
correlation,  decimation,  m-sequences,  p-ary sequences,  sequence family,  

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Based on the work by Helleseth [1], for an odd prime p and an even integer n=2m, the cross-correlation values between two decimated m-sequences by the decimation factors 2 and 4pn/2-2 are derived. Their cross-correlation function is at most 4-valued, that is, $igg { rac{-1 pm p^{n/2}}{2}, rac{-1 + 3p^{n/2}}{2}, rac{-1 + 5p^{n/2}}{2} igg }$. From this result, for pm ≠ 2 mod 3, a new sequence family with family size 4N and the maximum correlation magnitude upper bounded by $ rac{-1 + 5p^{n/2}}{2} simeq rac{5}{sqrt{2}}sqrt{N}$ is constructed, where $N = rac{p^n-1}{2}$ is the period of sequences in the family.