Two error-correcting pooling designs from symplectic spaces over a finite field
A binary matrix \(M\) is called \textit{\(s^e\)-disjunct} if given any \(s+1\) columns of \(M\) with one designated, there are \(e\) rows with a 1 in the designated column and 0 in each of the other \(s\) columns. In this article, two classes of \(s^e\)-disjunct matrices with subspaces in a symplectic space \(\mathbb{F}_q^{(2v)}\) are constructed and their disjunct properties are presented. The motivation for the construction of these classes arises from the use of such classes of matrices in pooling designs. For a pooling design, the smaller the number of tests, the better the pooling design is. To investigate this in relation to the classes the authors construct, the authors define the \textit{ratio} between the number of tests and the number of detected items test efficiency, that is, the ratio between the number of rows and the number of columns in the \(s^e\)-disjunct matrix, discuss this for their constructed classes and compare their ratio with other classes.
scientific article; zbMATH DE number 5775695