Periodic autocorrelation of sequences

The autocorrelation of a sequence is a useful criterion, among all, of resistance to cryptographic attacks. The behavior of the autocorrelations of random Boolean functions (studied by Florian Caullery, Eric F\'erard and Fran\c{c}ois Rodier [4]) shows that they are concentrated around a point. We show that the same is true for the evaluation of the periodic autocorrelations of random binary sequences.