*URN to cite this document:*urn:nbn:de:bvb:703-epub-4470-2

## Title data

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

**Subspace Packings : Constructions and Bounds.**

Bayreuth
,
2019
. - 34 S.

PDF
SubPack_rev.pdf - Published Version Available under License Creative Commons BY 4.0: Attribution . Download (451kB) |

## Abstract

The Grassmannian G_q(n,k) is the set of all k-dimensional subspaces of the vector space GF(q)^n. 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 G_q(n,k) also form a family of q-analogs of block designs and they are called 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 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 subspace packing t-(n,k,lambda)^m_q is a set S of k-dimensional subspaces from G_q(n,k) such that each t-dimensional subspace of G_q(n,t) is contained in at most lambda elements of S. The goal of this work is to consider the largest size of such subspace packings.