The paper gives lower bounds for the minimum number of weighings that are necessary for identi cation of up to non-standard objects out of the total number of objects being tested. For the problem with xed deviation of weights of non-standard objects we construct a perfect algorithms with parameters = 11, = 5, = 2 corresponding to the parameters of the ternary Virtakallio-Golay code. The nonexistence of a perfect weighing code with such parameters is proved.

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In this article we study the analysis and optimization principles of parameters and the mode of use the error-correcting code in the information transmission system with a reverse channel, which functions under the influence of intentional interference, its structure can be selected from the position of violation (deterioration) of the system operating. We see the developed methodology for optimizing system parameters according to the criterion of the maximum guaranteed information transfer rate for interference classes with limited average power. An assessment of the efficiency gain provided by applying the proposed optimizing methods of the channel block structure and its decoding mode is made.

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We study conditions for the existence of coalition games with the result invariant under cyclic shifts of players sequence numbers. Given a total number