A.N. Leukhin, N.V. Parsaev, L.G. Kornilova

The system of the nonlinear trigonometrical equations for synthesis of like-noise phase-coded sequences with one-level cyclic autocorrelation function is considered. For solving transition to system of the algebraic equations of high degrees is used. It is shown, that Galois group of roots of each equation is solvable group isomorphic to some polycyclic group of corresponding linear transformations. The example of solving of system of the equations using the developed method is resulted. The offered analytical method of the decision of system of the nonlinear equations allows to solve problem of synthesis of all possible phase-coded sequences with arbitrary level of side lobes of one-level cyclic ACF. Graphic representations of examples of the synthesized code sequences are resulted. «Movement trajectories» of last elementary vector as a part of code sequence in a complex plane are considered. Concepts of bifurcate points and singularity points are entered on considered curves. Analytical expressions for synthesis of new phase-coded sequences with one-level cyclic autocorrelation function are resulted