On the Crosscorrelation of Sequences with the Decimation Factor

Abstract.

Let p be a prime with p≡3 (mod 4), let n be an odd natural number and let . Consider the crosscorrelation funtion C _d (t)=∑ _{i =1} ^pn−1ζ^{ai − adi−t} where ζ≠1 is a complex p-th root of unity and (a _i ) is a maximal linear shift register sequence. In 7 the bound has been computed for p = 3. In this note we generalize this to for p≥ 3. Furthermore we giv an upper bound for the probability of the crosscorrelation function achieving the maximum absolute value.