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A new series of large sets of subspace designs over the binary field

Title data

Kiermaier, Michael ; Laue, Reinhard ; Wassermann, Alfred:
A new series of large sets of subspace designs over the binary field.
In: Designs, Codes and Cryptography. Vol. 86 (February 2018) Issue 2 . - pp. 251-268.
ISSN 0925-1022
DOI: https://doi.org/10.1007/s10623-017-0349-1

Project information

Project title:
Project's official titleProject's id
Random Network Coding and Designs over GF(q)IC1104

Project financing: COST – European Cooperation in Science and Technology

Abstract in another language

In this article, we show the existence of large sets LS_2[3](2,k,v) for infinitely many values of k and v. The exact condition is v ≥ 8 and 0 ≤ k ≤ v such that for the remainders v' and k' of v and k modulo 6 we have 2 ≤ v' ≤ k' ≤ 5.

The proof is constructive and consists of two parts. First, we give a computer construction for an LS_2[3](2,4,8), which is a partition of the set of all 4-dimensional subspaces of an 8-dimensional vector space over the binary field into three disjoint 2-(8, 4, 217)_2 subspace designs. Together with the already known LS_2[3](2,3,8), the application of a recursion method based on a decomposition of the Graßmannian into joins yields a construction for the claimed large sets.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Large set; Subspace design; Recursion; Method of Kramer and Mesner
Subject classification: Mathematics Subject Classification Code: 05B05 05B25 51E05
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 21 Jun 2018 05:24
Last Modified: 21 Jun 2018 05:24
URI: https://eref.uni-bayreuth.de/id/eprint/44593