A new construction of 3-separable matrices via an improved decoding of Macula's construction

Abstract

Macula proposed a novel construction of pooling designs which can effectively identify positive clones and also proposed a decoding method. However, the probability of all unresolved positive clone is hard to analyze. In this paper we propose an improved decoding method and show that ford d = 3 an exact probability analysis is possible. Further, we derive necessary and Sufficient conditions for a positive clone to be unresolved and gave a modified construction which avoids this necessary condition, thus resulting; in a 3-separable matrix. (c) 2008 Elsevier B.V. All rights reserved.