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Subspace packings : constructions and bounds

Title data

Etzion, Tuvi ; Kurz, Sascha ; Otal, Kamil ; Özbudak, Ferruh:
Subspace packings : constructions and bounds.
In: Designs, Codes and Cryptography. Vol. 88 (2020) . - pp. 1781-1810.
ISSN 1573-7586

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: random network coding; subspace codes; packings; designs; q-analogs
Subject classification: Mathematics Subject Classification Code: 51E20 (11T71 94B25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties > Faculty of Mathematics, Physics und Computer Science
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 14 Sep 2020 12:28
Last Modified: 23 Nov 2022 08:54