Matrix Approach to Binary Code Sequences Optimization for Noise Immune Communication Systems

The paper considers the problem of synthesis of code binary sequences (CBS) with optimal aperiodic autocorrelation functions according to the criterion of at least 4 levels of side lobes of the corresponding aperiodic autocorrelation function. The properties of algebraic operations in the finite fields are used to represent the above code binary sequences, their elements, and the convolution. The matrix, which determines the dependence between signs plus and minus of the elements of the binary sequences, also provide the possibility of establishing interrelation of the above-mentioned levels of side lobes. For the sequences of small dimensions, as an illustration, the analytical expressions of the specified relationship are given. The algorithm is substantiated and suggested, an example of synthesis of code binary sequences is given.