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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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