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New applications and results of superimposed code theory arising from the potentialities of molecular biology. (English) Zbl 1034.94015
Althöfer, Ingo (ed.) et al., Numbers, information and complexity. Dedicated to Rudolf Ahlswede on the occasion of his 60th birthday. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-7765-6/hbk). 265-282 (2000).
Summary: Superimposed codes (SC) were introduced by W. Kautz and R. Singleton [IEEE Trans. Inf. Theory 10, 363–377 (1964; Zbl 0133.12402)] who worked out the important constructive methods. A. D’yachkov and V. Rykov [Probl. Control Inf. Theory 12, 229–242 (1983; Zbl 0524.94016)] and P. Erdős, P. Frankl and Z. Füredi [Isr. J. Math. 51, 79–89 (1985; Zbl 0587.05021)] obtained upper and lower bounds on the rate of SC. D’yachkov, Macula and Rykov investigated the development of constructions for SC (nonadaptive pooling designs) intended for the clone-library screening problem. 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.
For the entire collection see [Zbl 0933.00056].

94B60 Other types of codes
92D20 Protein sequences, DNA sequences
94B25 Combinatorial codes
94B05 Linear codes (general theory)