Browsing by Author "Vilenkin, P"

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A construction of pooling designs with some happy surprises
(2005-10-01)
D'yachkov, A
;
Hwang, F
;
Macula, A
;
Vilenkin, P
;
Weng, CW
The screening of data sets for "positive data objects" is essential to modern technology. A ( group) test that indicates whether a positive data object is in a specific subset or pool of the dataset can greatly facilitate the identification of all the positive data objects. A collection of tested pools is called a pooling design. Pooling designs are standard experimental tools in many biotechnical applications. In this paper, we use the ( linear) subspace relation coupled with the general concept of a "containment matrix" to construct pooling designs with surprisingly high degrees of error correction ( detection.) Error-correcting pooling designs are important to biotechnical applications where error rates often are as high as 15%. What is also surprising is that the rank of the pooling design containment matrix is independent of the number of positive data objects in the dataset.