Coding Theory at the Department of Probability Theory

Suppose that among a large set of factors there is a small subset of significant factors. The problem of screening experiments design is to find all significant factors by carrying out group tests on properly chosen subsets of the set of factors. The test outcome is positive if the testing group contains one or more significant elements; otherwise, it is negative. Our goal is to design the minimal number of such group tests.
The topic has been treated extensively. The analogies of Shannon's theorem were proved by Malyutov M. and Freidlina V. (1975). Some underlying results for a combinatorial model were established by D'yachkov A., Rykov V., and Vilenkin P. (1982, 1989, 2000, 2002). We discuss the subsequent development of the field. In particular, we focus on lower and upper bounds of asymptotic rates for designs (codes) arising naturally for solving problems in the given area.
The present talk is based on the joint work with D'yachkov A., Vorobyev I., and Shchukin V.