Naslov
Q-analogs of group divisible designs

Autori
Buratti, Marco ; Kiermaier, Michael ; Kurz, Sascha ; Nakić, Anamari ; Wassermann, Alfred

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Combinatorics and Finite Fields

Urednik/ci
Schmidt, Kai-Uwe ; Winterhof, Arne

Izdavač
Walter de Gruyter

Grad
Berlin

Godina
2019

Raspon stranica
21-38

ISBN
978-3-11-064179-0

Ključne riječi
Combinatorics ; Finite Fields ; Difference Sets ; Polynomials ; Pseudorandomness

Sažetak
A well-known class of objects in combinatorial design theory are group divisible designs. Here, we introduce the q-analogs of group divisible designs. It turns out that there are interesting connections to scattered subspaces, q-Steiner systems, packing designs and qr- divisible projective sets. We give necessary conditions for the existence of q-analogs of group divisible designs, construct an infinite series of examples and provide further existence results with the help of a computer search. One example is a (6, 2, 3, 2)_2 group divisible design over GF(2) which is a packing design consisting of 180 blocks that such every 2-dimensional subspace in GF(2)^6 is covered at most twice.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA