New Applications and Results of Superimposed Code Theory Arising from the Potentialities of Molecular Biology

Superimposed codes (SC) were introduced by Kautz-Singleton (1964) [1], who worked out the important constructive methods. Dyachkov-Rykov [2, 3, 4, 5, 6] and Erdos-Frankl-Furedi [7] obtained upper and lower bounds on the rate of SC. Dyachkov-Macula-Rykov [8, 9, 10, 11] investigated the development of constructions for SC (nonadaptive pooling designs) intended for the clone-library screening problem. (See Balding-Torney [12] and Knill-Bruno-Torney [13]). In this paper, we give an introduction to the problem and a detailed survey of our recent results on constructive methods of SC. We discuss superimposed distance codes and list-decoding superimposed codes.

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