6,901 research outputs found
A review of Costas arrays
Costas arrays are not only useful in radar engineering, but they
also present many interesting, and still open, mathematical
problems. This work collects in it all important knowledge about
them available today: some history of the subjects, density
results, construction methods, construction algorithms with full
proofs, and open questions. At the same time all the necessary
mathematical background is offered in the simplest possible format
and terms, so that this work can play the role of a reference for
mathematicians and mathematically inclined engineers interested in the field
Construction of nested space-filling designs
New types of designs called nested space-filling designs have been proposed
for conducting multiple computer experiments with different levels of accuracy.
In this article, we develop several approaches to constructing such designs.
The development of these methods also leads to the introduction of several new
discrete mathematics concepts, including nested orthogonal arrays and nested
difference matrices.Comment: Published in at http://dx.doi.org/10.1214/09-AOS690 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
Absolutely Maximally Entangled (AME) states are those multipartite quantum
states that carry absolute maximum entanglement in all possible partitions. AME
states are known to play a relevant role in multipartite teleportation, in
quantum secret sharing and they provide the basis novel tensor networks related
to holography. We present alternative constructions of AME states and show
their link with combinatorial designs. We also analyze a key property of AME,
namely their relation to tensors that can be understood as unitary
transformations in every of its bi-partitions. We call this property
multi-unitarity.Comment: 18 pages, 2 figures. Comments are very welcom
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