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On the crosscorrelation of sequences over GF(p) with short periods

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1 Author(s)
E. N. Muller ; Fakultat fur Math., Otto-von-Guericke-Univ., Magdeburg, Germany

We investigate the crosscorrelation function Cd(t)=Σi=1 (pn-1) ζ(ai-t-adi), where ζ is a complex primitive pth root of unity, (ai)(i∈N0) is a maximal linear shift-register sequence of length pn-1, and p is an odd prime. For p=3, n odd, and d=pn+1/4+pn-1/2 we show that 2·√pn is an upper bound for the absolute value of 1+Cd(t). For any odd prime p and pk+1, where n/gcd/(n,k) is not divisible by 4 we determine the maximum absolute value of Cd(t) and the number of values of Cd(t)

Published in:

IEEE Transactions on Information Theory  (Volume:45 ,  Issue: 1 )