Families of finite sets in which no intersection of l sets is covered by the union of s others

摘要

In 1964, Kautz and Singleton (IEEE Trans. Inform. Theory 10 (1964), 363-377) introduced the superimposed code concept. A binary superimposed code of strength s is identified by the incidence matrix of a family of finite sets in which no set is covered by the union of s others (J Combin. Theory Ser. A 33 (1982), 158-166 and Israel J Math. 51 (1985), 75-89). In the present paper, we consider a generalization called a binary superimposed (s, l)-code which is identified by the incidence matrix of a family defined in the title. We discuss the constructions based on MDS-codes (The Theory of Error-correcting Codes, North-Holland, Amsterdam, The Netherlands, 1983) and derive upper and lower bounds on the rate of these codes. (C) 2002 Elsevier Science (USA). [References: 21]