Low autocorrelated multiphase sequences.
The interplay between the ground-state energy of the generalized Bernasconi model to multiphase, and the minimal value of the maximal autocorrelation function, C(max)=max(K)/C(K)/, K=1,...,N-1, is examined analytically in the thermodynamic limit where the main results are (a) For the binary case, the minimal value of C(max) over all sequences of length N, minC(max), is 0.435sqrt[N], significantly smaller than the typical value for random sequences O(sqrt[log N]sqrt[N]). (b) A new method to approximate F(max) is obtained using the observation of data collapse. (c) minC(max) is obtained in an energy which is about 30% above the ground-state energy of the generalized Bernasconi model, independent of the number of phases m. (d) For a given m, minC(max) proportional sqrt[N/m] indicating that for m=N, minC(max)=1, i.e., a generalized Barker code exists. The analytical results are confirmed by simulations.
Ein-Dor
Liat
L
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel.
Kanter
Ido
I
Kinzel
Wolfgang
W