THE SEARCH ALGORITHM, SOME PROPERTIES AND APPLICATIONS OF MATRICES
WITH COMPLEX VALUES OF THE ELEMENTS FOR STEGANOGRAPHY AND SYNTHESIS OF
WIDEBAND SIGNALS

A. Y. Grishentcev ** **^{1},
A. G. Korobeynikov **
**^{2}

** **^{1}
Saint Petersburg National Research University of Information
Technologies, Mechanics and Optics

**
**^{2}
Pushkov institute of terrestrial magnetism, ionosphere and radio wave
propagation of the Russian Academy of Sciences St.-Petersburg Filial

The paper is
received on May 3, 2016

**
Abstract. **
An investigation of some properties of matrices and methods of
synthesis of particular form of the autocorrelation function is carried out.
The elements of such matrices are complex numbers with the module equal to one.
The aim is to fins and to study some properties of matrices with a special form
of the autocorrelation function. These matrices allow to increase the number of
symbols of the alphabet code sequences; to increase the energy density of the
synthesized wideband signal; to pursue opportunities hidden messaging. Authors
have developed a method of finding the matrix of a given size on the basis of
combinatorial sorting options and check the values of the autocorrelation function. We developed and optimized
combinatorial search algorithm, investigated some properties of matrices with a
special form of the autocorrelation function. We have developed a computer
program which permits to found some matrix with a particular form of the
autocorrelation function, and given their characteristics. Considerable
attention is given to the classification of the found matrices and their
comparison with some common code sequences, eg, Barker codes. An example of the
practical use of the matrix with a particular form of the autocorrelation
function is given. The matrix classes with a special form of the
autocorrelation function provides significant opportunities for hidden messaging
in a variety of containers: from the radio broadcast to digital images. The
publication contains a significant number of practical material illustrated by
comparative tables and displays various waveform graphs and charts. The studies
have shown: the number of the found matrix is sufficiently large that provides opportunities for the formation of
a much larger message of the alphabet, for example, than using Barker codes or
Hadamard matrices. A significant number of the found matrices allows us to
implement additional features, such as encryption of transmitted messages due
to the change of the alphabet according to a pseudorandom, known beforehand on
the transmitting and receiving sides. The proposed methods in computational
optimization allowed to increase significantly the speed of finding the
matrices with a special form of the autocorrelation function. Additional
information may be found on the site of one of the authors:
http://www.moveinfo.ru/.

**
Keywords:** matrix, code division signals, radio, steganography, the
autocorrelation function, wideband.