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Frontiers of Electrical and Electronic Engineering

ISSN 2095-2732

ISSN 2095-2740(Online)

CN 10-1028/TM

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Front Elect Electr Eng    2012, Vol. 7 Issue (3) : 308-311    https://doi.org/10.1007/s11460-012-0205-z
RESEARCH ARTICLE
New classes of sequence families with low correlation by using multiplicative and additive characters
Pinhui KE(), Shengyuan ZHANG
Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou 350007, China
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Abstract

For an odd prime p, a new sequence family of period pm-1, size (M-1)pmr is proposed using multiplicative and additive characters. The upper bound for the maximum magnitude of nontrivial correlations of the sequence family is derived using well-known character sums. The upper bound is shown to be (r+1)pm+3, which meets the Welch bound asymptotically.
Keywords finite field      character sum      correlation      polyphase sequence      Welch bound     
Corresponding Author(s): KE Pinhui,Email:keph@fjnu.edu.cn   
Issue Date: 05 September 2012
 Cite this article:   
Pinhui KE,Shengyuan ZHANG. New classes of sequence families with low correlation by using multiplicative and additive characters[J]. Front Elect Electr Eng, 2012, 7(3): 308-311.
 URL:  
https://academic.hep.com.cn/fee/EN/10.1007/s11460-012-0205-z
https://academic.hep.com.cn/fee/EN/Y2012/V7/I3/308
period LalphabetRmaxfamily size
F ?r [3]PM2L+5(M+1)(L+1)2
Fr[3]PM3L+4(M-1)2(L-1)2+(M-1)
Fs[3]pm-1M2L+1+6(M-1)L2+?M-12?
L [8]pm-1M3L+1+5(M-1)2(L-2)2+M(M-1)2
V [4]pm-1M3L+1+1(M-1)?(L2+1)
U [4]pm-1M3L+1+5M(M-1)(L-1)2+M-1
Fok(ρ)[9]pm-1P1+pm+(2ρ-1)e2pme
Ωr[5]Pp(p-1)(r+1)p+2(p-2)?pr
Γr(this paper)pm-1Mp(r+1)pm+3(M-1)?pmr
Tab.1  Comparison of several classes of sequence families with low correlation and large family size
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