28,748 research outputs found
Covering of Subspaces by Subspaces
Lower and upper bounds on the size of a covering of subspaces in the
Grassmann graph \cG_q(n,r) by subspaces from the Grassmann graph
\cG_q(n,k), , are discussed. The problem is of interest from four
points of view: coding theory, combinatorial designs, -analogs, and
projective geometry. In particular we examine coverings based on lifted maximum
rank distance codes, combined with spreads and a recursive construction. New
constructions are given for with or . We discuss the density
for some of these coverings. Tables for the best known coverings, for and
, are presented. We present some questions concerning
possible constructions of new coverings of smaller size.Comment: arXiv admin note: text overlap with arXiv:0805.352
Covering Numbers in Linear Algebra
We compute the minimal cardinality of a covering (resp. an irredundant
covering) of a vector space over an arbitrary field by proper linear subspaces.
Analogues for affine linear subspaces are also given.Comment: 4 page
Formal concept analysis and structures underlying quantum logics
A Hilbert space induces a formal context, the Hilbert formal context , whose associated concept lattice is isomorphic to the lattice of closed subspaces of . This set of closed subspaces, denoted , is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called ``propositional system'', that is, a complete, atomistic, orthomodular lattice which satisfies the covering law.
In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of of Chu correspondences between Hilbert contextsUniversidad de Málaga. Campus de Excelencia Internacional AndalucÃa Tech
An extremal problem for integer sparse recovery
Motivated by the problem of integer sparse recovery we study the following
question. Let be an integer matrix whose entries are in
absolute value at most . How large can be if all
submatrices of are non-degenerate? We obtain new upper and lower bounds on
and answer a special case of the problem by Brass, Moser and Pach on
covering -dimensional grid by linear subspaces
Problems on q-Analogs in Coding Theory
The interest in -analogs of codes and designs has been increased in the
last few years as a consequence of their new application in error-correction
for random network coding. There are many interesting theoretical, algebraic,
and combinatorial coding problems concerning these q-analogs which remained
unsolved. The first goal of this paper is to make a short summary of the large
amount of research which was done in the area mainly in the last few years and
to provide most of the relevant references. The second goal of this paper is to
present one hundred open questions and problems for future research, whose
solution will advance the knowledge in this area. The third goal of this paper
is to present and start some directions in solving some of these problems.Comment: arXiv admin note: text overlap with arXiv:0805.3528 by other author
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