Slobodian M. Approximation of distribution of the number of false solutions of the system of nonlinear random equations in the field GF(2) by Poisson distribution.

The thesis is devoted to the further development of the theory of systems of nonlinear random equations over the field GF(2). The distribution of a number of false solutions (i.e. solutions that differ from some fixed solution) of the system of nonlinear random equations in the field GF(2) by Poisson distribution is investigated. The estimates of the approximation's rate and order of approximation's rate of the distribution of a number of false solutions of the system of nonlinear random equations in the field GF(2) by Poisson distribution under the condition that the number of non-zero components of the fixed solution of system increases as number of unknown variables n increases are obtained. The estimates of the approximation's rate and order of approximation's rate of the distribution of a number of false solutions of the system of nonlinear random equations in the field GF(2) by Poisson distribution are derived when the system has a linear part with positive probability are obtained. The estimates of the approximation's rate and order of approximation's rate of the distribution of a number of false solutions of the system of nonlinear random equations in the field GF(2) by Poisson distribution under the condition that the number of zero components of the fixed solution of system increases as n increases. Examples showing that the obtained estimates are non-trivial are presented. Obtained results are both of theoretical and practical interest, in particular, for problems of information encoding at transfer by communication channels and guarding against the unauthorized access.