160 research outputs found
More nonexistence results for symmetric pair coverings
A -covering is a pair , where is a
-set of points and is a collection of -subsets of
(called blocks), such that every unordered pair of points in is contained
in at least blocks in . The excess of such a covering is
the multigraph on vertex set in which the edge between vertices and
has multiplicity , where is the number of blocks which
contain the pair . A covering is symmetric if it has the same number
of blocks as points. Bryant et al.(2011) adapted the determinant related
arguments used in the proof of the Bruck-Ryser-Chowla theorem to establish the
nonexistence of certain symmetric coverings with -regular excesses. Here, we
adapt the arguments related to rational congruence of matrices and show that
they imply the nonexistence of some cyclic symmetric coverings and of various
symmetric coverings with specified excesses.Comment: Submitted on May 22, 2015 to the Journal of Linear Algebra and its
Application
Compressed sensing with combinatorial designs: theory and simulations
In 'An asymptotic result on compressed sensing matrices', a new construction
for compressed sensing matrices using combinatorial design theory was
introduced. In this paper, we use deterministic and probabilistic methods to
analyse the performance of matrices obtained from this construction. We provide
new theoretical results and detailed simulations. These simulations indicate
that the construction is competitive with Gaussian random matrices, and that
recovery is tolerant to noise. A new recovery algorithm tailored to the
construction is also given.Comment: 18 pages, 3 figure
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