Subspace Packings

Date

2019-03-31

Author

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

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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.

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

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Department of Mathematics, Conference / Seminar

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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.