A refined formula for the autocorrelation function of an M-sequence

We consider a widespread impreciseness in the autocorrelation function formula for M-sequences. We propose a derivation of the exact expression for the normalized autocorrelation function for a $p$-ary sequence in almost all points of the temporal argument inside a period. We justify the value balance property for the periodic autocorrelation function that lets us obtain analytic expressions for peak outliers of the autocorrelation inside a minimal period for ternary and quinary M-sequences.

Presented by the member of Editorial Board: L. A. Mironovskii