Superimposed codes and threshold group testing

Authors:
Arkadii D'yachkov;Vyacheslav Rykov;Christian Deppe;Vladimir Lebedev
Affiliations:
Faculty of Mechanics and Mathematics, Department of Probability Theory, Moscow State University, Moscow, Russia;Department of Mathematics, University of Nebraska at Omaha, Omaha, NE;Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany;IPPI Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
Venue:
Information Theory, Combinatorics, and Search Theory
Year:
2013

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Abstract

We will discuss superimposed codes and non-adaptive group testing designs arising from the potentialities of compressed genotyping models in molecular biology. The given paper was motivated by the 30th anniversary of D'yachkov-Rykov recurrent upper bound on the rate of superimposed codes published in 1982. We were also inspired by recent results obtained for non-adaptive threshold group testing which develop the theory of superimposed codes.