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

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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(pS) 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 α and α^2 , where α is a primitive element of field GF(p^S), the minimal polynomials of elements α and α^(i_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.

About the authors

V. G. Starodubtsev

Mozhaysky Military-Space Academy

Author for correspondence.
Email: vgstarod@mail.ru
St. Petersburg, 197198 Russia

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