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

We investigate the crosscorrelation function Cd(t)=Σ_i=1 (p^n-1) ζ(a^i-t-a^di), where ζ is a complex primitive pth root of unity, (a_i)(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+C_d(t). For any odd prime p and p^k+1, where n/gcd/(n,k) is not divisible by 4 we determine the maximum absolute value of C_d(t) and the number of values of C_d(t)