# zbMATH — the first resource for mathematics

A simple construction of $$d$$-disjunct matrices with certain constant weights. (English) Zbl 0870.05012
Summary: We give a simple method of constructing $$d$$-disjunct matrices. For $$k>d$$, our construction yields an $${n\choose d}\times {n\choose k}$$ $$d$$-disjunct matrix with column weight $${k\choose d}$$ and row weight $${{n-d}\choose {k-d}}$$.

##### MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
Full Text:
##### References:
 [1] Du, D.; Hwang, F., Combinatorial group testing and its applications, (1993), World Scientific Singapore · Zbl 0867.90060 [2] A. Dyachkov and V. Rykov, A survey of superimposed code theory, Problems Contr. Inform. Theory 12(4) 1-13. [3] Erdös, P.; Frankl, P.; Furedi, Z., Families of finite sets in which no set is covered by the union of two others, J. combin. theory ser. A, 33, 158-166, (1982) · Zbl 0489.05003 [4] Erdös, P.; Frankl, P.; Furedi, Z., Families of finite sets in which no set is covered by the union of r others, Israel J. math., 51, 79-89, (1985) · Zbl 0587.05021 [5] Hwang, F.; Sos, V., Non-adaptive hypergeometric group testing, Studia sci. math. hung., 22, 257-263, (1987) · Zbl 0639.62076 [6] Katona, G., Renyi and the combinatorial search problems, Studia sci. math. hung., 26, 363-376, (1991) · Zbl 0788.68004 [7] Kautz, W.; Singleton, R., Nonrandom binary superimposed codes, IEEE trans. inform. theory, 10, 363-377, (1964) · Zbl 0133.12402 [8] Quang, A.; Zeisel, T., Bounds on constant weight binary superimposed codes, (), 223-230 · Zbl 0652.94021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.