Subspace Packing

Title data

Etzion, Tuvi ; Kurz, Sascha ; Otal, Kamil ; Özbudak, Ferruh:
Subspace Packing.
2019
Event: WCC 2019: The Eleventh International Workshop on Coding and Cryptography , 31.03.-05.04.2019 , Saint-Jacut-de-la-Mer, France.
(Conference item: Workshop , Speech )

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Abstract in another language

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 subspacepackings 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 pack-ing t-(n,k,λ)_q is a set S of k-subspaces from G_q(n,k) such that each t-subspace of G_q(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.