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《Acta Electronica Sinica》 2000-10
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On the Crosscorrelation of m Sequence over Finite Field and Its Decimation Sequence

ZHANG Zhen tao,SUN Wei,YANG Yi xian,HU Zheng ming,LI Xin (Information Security Center of Beijing Univ.of Posts and Telecomms P.O.Box 126,Beijing 1000876,China)  
In this paper we investigate the crosscorrelation function C d(t) of m sequence on finite field GF(p) and its decimation sequence,and get the following results:(1)For decimation factor d=p n+1p+1+p n-12,p ≡3(mod 4), n odd,we show that |1+C d(t)| 1+p2p n ,and therefore solve an open problem raised by Muller in [1] and generalize the result proved in [1];(2)For decimation factor d=p n+1p+1,n odd, p ≡3(mod 4),we show C d(t)∈{-1,-1+p n+1 ,-1-p n+1 }; (3)In the two cases above,we study the distribution of |1+ C d(t) | with respect to t ,and obtain that when p is big enough,the probability of |1+ C d(t) | achieving the maximum is very small.
【Fund】: 国家自然科学基金资助项目! (No .6980 2 0 0 2 ;69882 0 0 2 ;69772 0 35);; 国家“863”资助项目!(No .863 30 6 ZT0 5 0 5 2 ) ;国家重
【CateGory Index】: O236
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【References】
Chinese Journal Full-text Database 1 Hits
1 XU Xiang-yang Department of Computer Science and Technology,Changsha University,Changsha 410003,China;Cross-correlation of key m-sequences and its decimation sequence[J];Computer Engineering and Applications;2010-16
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 LIU Liao-yuan;Hanming Encoder and Hanming Decoder Based on VHDL Language Design[J];Journal of Anhui Vocational & Technical College;2006-04
2 ZOU Xue-yu YI Guo-hua (Yangtze University,Jingzhou 434023);A Kind of Design of M-sequence Generator Based on FPGA[J];;2006-03
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5 Zhou Xuan Li Chao Dept. of Mathematics and System Science, School of Science, NUDT, Changsha 410073, China) (Inst. of Network and Information Security, School of Compute, NUDT, Changsha 410073, China) (Lab. of Computer Science, Inst. of Software, Chinese Academy of Sciences, Beijing 100080, China);Auto-correlation Function of Generalized Jacobi Sequences[J];Journal of Electronics and Information Technology;2005-04
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