Optimal superimposed codes and designs for Renyi’s search model
نویسندگان
چکیده
Renyi (Bull. Amer. Math. Soc. 71 (6) (1965) 809) suggested a combinatorial group testing model, in which the size of a testing group was restricted. In this model, Renyi considered the search of one defective element (signi5cant factor) from the 5nite set of elements (factors). The corresponding optimal search designs were obtained by Katona (J. Combin. Theory 1 (2) (1966) 174). In the present work, we study Renyi’s search model of several signi5cant factors. This problem is closely related to the concept of binary superimposed codes, which were introduced by Kautz and Singleton (IEEE Trans. Inform Theory 10 (4) (1964) 363) and were investigated by D’yachkov and Rykov (Problems Control Inform. Theory 12 (4) (1983) 229), Erdos et al. (Israel J. Math. 51 (1–2) (1985) 75), Ruszinko (J. Combin. Theory Ser. A 66 (1994) 302) and Furedi (J. Combin. Theory Ser. A 73 (1996) 172). Our goal is to prove a lower bound on the search length and to construct the optimal superimposed codes and search designs. The preliminary results have been published by D’yachkov and Rykov (Conference on Computer Science & Engineering Technology, Yerevan, Armenia, September 1997, p. 242). c © 2002 Elsevier Science B.V. All rights reserved. MSC: 94B50
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