Title data
Etzion, Tuvi ; Kurz, Sascha ; Otal, Kamil ; Özbudak, Ferruh:
Subspace Packings : Constructions and Bounds.
Bayreuth
,
2019
.  34 S.
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Abstract
The Grassmannian G_q(n,k) is the set of all kdimensional subspaces of the vector space GF(q)^n. It is well known that codes in the Grassmannian space can be used for errorcorrection in random network coding. On the other hand, these codes are qanalogs 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 qanalogs of block designs and they are called subspace designs. The application of subspace codes has motivated extensive work on the qanalogs of block designs. In this paper, we examine one of the last families of qanalogs of block designs which was not considered before. This family called subspace packings is the qanalog 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 kdimensional subspaces from G_q(n,k) such that each tdimensional 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.
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 Subspace Packings : Constructions and Bounds. (deposited 16 Sep 2019 10:06) [Currently Displayed]