Subspace Packings

Date

2019-03-31

Author

Etzion, Tuvi
Kurz, Sascha
Otal, Kamil
Özbudak, Ferruh

Metadata

Show full item record

Item Usage Stats

228
views

0
downloads

The Grassmannian Gq(n,k) is the set of all k-dimensional subspaces of the vector space Fnq. It is well known that codes in the Grassmannian space can be used for error-correction in random network coding. On the other hand, these codes are q-analogs of codes in the Johnson scheme, i.e. constant dimension codes. These codes of the Grassmannian Gq(n,k) also form a family of q-analogs of block designs and they are called \emph{subspace designs}. The application of subspace codes has motivated extensive work on the q-analogs of block designs. In this paper, we examine one of the last families of q-analogs of block designs which was not considered before. This family called \emph{subspace packings} is the q-analog of packings. This family of designs was considered recently for network coding solution for a family of multicast networks called the generalized combination networks. A \emph{subspace packing} t-(n,k,λ)mq is a set S of k-subspaces from Gq(n,k) such that each t-subspace of Gq(n,t) is contained in at most λ elements of S. The goal of this work is to consider the largest size of such subspace packings.

URI

https://hdl.handle.net/11511/76679

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Subspace packings: constructions and bounds Etzion, Tuvi; Kurz, Sascha; Otal, Kamil; Özbudak, Ferruh (Springer Science and Business Media LLC, 2020-09-01) Grassmannian Gq (n, k) is the set of all k-dimensional subspaces of the vector space Fn q. Kotter and Kschischang showed that codes in Grassmannian space can be used for error-correction in random network coding. On the other hand, these codes are q-analogs of codes in the Johnson scheme, i.e. constant dimension codes. These codes of the Grassmannian Gq (n, k) also form a family of q-analogs of block designs and they are called subspace designs. In this paper, we examine one of the last families of q-analog...
Quasi-constricted linear operators on Banach spaces Wolff, MPH; Emel'yanov, Eduard Yu. (2001-01-01) Let X be a Banach space over C. The bounded linear operator T on X is called quasi-constricted if the subspace X-0 := {x epsilon X : lim(n --> infinity) parallel toT(n)x parallel to = 0} is closed and has finite codimension. We show that a power bounded linear operator T epsilon L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness chi parallel to (.)parallel to (1) (A) )over bar>T is mean ergodic for all lambda in the peripheral spectrum sigma (pi)(T) of T is constric...
Piecewise polynomials with different smoothness degrees on polyhedral complexes ALTINOK BHUPAL, SELMA; Sipahi, Neslihan Os (Informa UK Limited, 2019-05-01) For a given d-dimensional polyhedral complex Delta and a given degree k, we consider the vector space of piecewise polynomial functions on Delta of degree at most k with a different smoothness condition on each pair of adjacent d-faces of Delta. This is a finite dimensional vector space. The fundamental problem in Approximation Theory is to compute the dimension of this vector space. It is known that the dimension is given by a polynomial for sufficiently large k via commutative algebra. By using the techni...
Invariant subspaces for positive operators acting on a Banach space with Markushevich basis Ercan, Z; Onal, S (Springer Science and Business Media LLC, 2004-06-01) We introduce 'weak quasinilpotence' for operators. Then, by substituting 'Markushevich basis' and 'weak quasinilpotence at a nonzero vector' for 'Schauder basis' and 'quasinilpotence at a nonzero vector', respectively, we answer a question on the invariant subspaces of positive operators in [ 3].
Quasi constricted linear representations of abelian semigroups on Banach spaces Emelyanov, Eduard (2002-07-24) Let (X, ∥·∥) be a Banach space. We study asymptotically bounded quasi constricted representations of an abelian semigroup IP in L(X), i.e. representations (Tt)t∈IP which satisfy the following conditions: i) limt→∞ ∥Ttx∥ < ∞ for all x ∈ X. ii) X0:= {x ∈ X:limt→∞ ∥Ttx∥ = 0} is closed and has finite codimension. We show that an asymptotically bounded representation (Tt)t∈IP is quasi constricted if and only if it has an attractor A with Hausdorff measure of noncompactness X∥·∥1 (A) < 1 with respect to some equi...

Citation Formats

T. Etzion, S. Kurz, K. Otal, and F. Özbudak, “Subspace Packings,” 2019, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/76679.