Pooling spaces associated with finite geometry

AbstractMotivated by the works of Ngo and Du [H. Ngo, D. Du, A survey on combinatorial group testing algorithms with applications to DNA library screening, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55 (2000) 171–182], the notion of pooling spaces was introduced [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Mathematics 282 (2004) 163–169] for a systematic way of constructing pooling designs; note that geometric lattices are among pooling spaces. This paper attempts to draw possible connections from finite geometry and distance regular graphs to pooling spaces: including the projective spaces, the affine spaces, the attenuated spaces, and a few families of geometric lattices associated with the orbits of subspaces under finite classical groups, and associated with d-bounded distance-regular graphs

Metrics on permutations, a survey

Abstract: This is a survey on distances on the symmetric groups Sn together with their applications in many contexts; for example: statistics, coding theory, computing, bell-ringing and so on, which were originally seen unrelated. This paper initializes a step of research toward this direction in the hope that it will stimulate more researchs and eventually lead to a systematic study on this subject. Distances on Sn were used in many papers in different contexts; for example, in statistics (see [Cr] and its references), coding theory (see [BCD] and its references), in computing (see, for example [Kn]), bell-ringing and so on. Here we attempt to give a brief bird’s view of distances on Sn according to types of problems considered

A Generalization Of Strongly Regular Graphs

: Motivated from an example of ridge graphs of metric polytopes, we consider a class of connected regular graphs such that the squares of their adjacency matrices lies in some symmetric Bose-Mesner algebras of dimension 3, as a generalization of strongly regular graphs. In addition to a detailed analysis of this prototype example defined over (MetP 5 ) , some general properties of these graphs are studied from the combinatorial view point. 1 . Introduction The notion of ridge graphs is given in [3] for studying metric polytopes MetP n and their relatives. The complement of one of those is interesting to us in this paper. Indeed, after some modifications, a connected regular graph is found such e-mail:[email protected] that the square of its adjacency matrix lies in a symmetric Bose-Mesner algebra of dimension 3, though itself is not strongly regular. It therefore leads to another interesting generalization of strongly regular graphs besides the notion of distance regular g..

Two error-correcting pooling designs from symplectic spaces over a finite field

AbstractIn this paper, we construct two classes of t×n,se-disjunct matrix with subspaces in a symplectic space Fq(2ν) and prove that the ratio efficiency t/n of two constructions are smaller than that of D’yachkov et al. (2005) [2]