On the odd and the aperiodic correlation properties of the Kasami sequences

Derives a new upper bound for the odd and the aperiodic correlations of binary sequences in the small Kasami family. The approach is based on a technique described in S. Litsyn and A. Tietavainen (1994) that is originally due to I.M. Vinogradov (1954). An essential ingredient in this method is a good upper bound on the discrete Fourier coefficients of a shifted product of a pair of sequences. The author obtains an upper bound of the order O(√LlnL) for the maximal aperiodic and odd correlation magnitudes for sequences of length L