Subspace packings: constructions and bounds

Date

2020-09-01

Author

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

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

245
views

0
downloads

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-analogs of block designs which was not considered before. This family called subspace packings is the q-analog of packings, and was considered recently for network coding solution for a family of multicast networks called the generalized combination networks. A subspace packing t-(n, k,.) q 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. elements of S. The goal of this work is to consider the largest size of such subspace packings. We derive a sequence of lower and upper bounds on the maximum size of such packings, analyse these bounds, and identify the important problems for further research in this area.

Subject Keywords

Applied Mathematics, Computer Science Applications

URI

https://hdl.handle.net/11511/34314

Journal

DESIGNS CODES AND CRYPTOGRAPHY

DOI

https://doi.org/10.1007/s10623-020-00732-z

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

ON THE NUMERICAL EVALUATION OF AN OSCILLATING INFINITE SERIES-III Tezer, Münevver (Informa UK Limited, 1990-01-01) An oscillating infinite series involving product of Bessel function J o(x) and an oscillating infinite series involving trigonometric function sin(x) were evaluated and computed numerically in [1] and [2] respectively. In this paper, an oscillating infinite series involving product of exponential, Bessel and trigonometric functions is evaluated. The series is transformed first into the sum of two infinite integrals by using contour integration and then the infinite integral with oscillating integrand is tra...
Holomorphic extension of meromorphic mappings along real analytic hypersurfaces Yazıcı, Özcan (Springer Science and Business Media LLC, 2020-08-01) Let M subset of C-n be a real analytic hypersurface, M' subset of C-N (N >= n) be a strongly pseudoconvex real algebraic hypersurface of the special form, and F be a meromorphic mapping in a neighborhood of a point p is an element of M which is holomorphic in one side of M. Assuming some additional conditions for the mapping F on the hypersurface M, we proved that F has a holomorphic extension to p. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensi...
Legendrian realization in convex Lefschetz fibrations and convex stabilizations Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01) We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on partial derivative W, can be assumed to be Legendrian in partial derivative W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also s...
Subspace Packings Etzion, Tuvi; Kurz, Sascha; Otal, Kamil; Özbudak, Ferruh (2019-03-31) 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...
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications Ercan, Z (American Mathematical Society (AMS), 2004-01-01) We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).

Citation Formats

T. Etzion, S. Kurz, K. Otal, and F. Özbudak, “Subspace packings: constructions and bounds,” DESIGNS CODES AND CRYPTOGRAPHY, pp. 1781–1810, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34314.