Sets of Nonbinary Sequences with a Low Level of Mutual Correlation for Systems of Digital Information Transmission

Abstract

The sets of nonbinary pseudorandom sequences (NPSs) for periods N = p^S – 1 < 20 000 (p = 3, 5, 7, and 11) generated in finite fields GF(p^S) whose power is V = N + 1 and the maximum of the module of peaks of the periodic autocorrelation function (PACF) and periodic cross-correlation function (PCCF) satisfy the bounds obtained by Sidel’nikov. In addition to the minimal polynomials of elements ${{\alpha }}$ and ${{{{\alpha }}}^{2}}$, where α is a primitive element of field GF(p^S), the minimal polynomials of elements ${{\alpha }}$ and ${{{{\alpha }}}^{{{{i}_{{\text{d}}}}}}}$ (i_d is the decimation index) are determined on the basis of which the new sets of NPSs can be formed with the equivalent correlation properties. Sets of indices i_d > 2 are determined for various combinations of parameters p and S. The cases of even and odd values of parameter S are considered, for which the values of the PACF and PCCF with the maximum module are obtained and the number and values of different levels of correlation functions are determined.