Sequences with small aperiodic correlations in the vicinity of the zero shift

The paper addresses a problem of designing sequences with small aperiodic autocorrelations and crosscorrelations within a given window around the zero shift. We provide a systematic method for constructing mutually orthogonal sequences of length N so that all j-th aperiodic autocorrelations and all j-th crosscorrelations are bounded above by j/N, 1 ≤ j < d where d ≪ N is a given parameter. Furthermore, we prove a tight upper bound on a number of sequences, whose all aperiodic correlations are zero within the window {-d + 1, ..., d - 1) except for the autocorrelation at the origin. Such sequences are used in LAS-CDMA (Large Area Synchronized - Code Division Multiple Access), a new CDMA-system proposed as the basis for all future wireless communications.