Name
Abstract | ||
|---|---|---|
In this article, we investigate collections of ‘well-spread-out’ projective (and linear) subspaces. Projective -subspaces in are in ‘higgledy-piggledy arrangement’ if they meet each projective subspace of co-dimension in a generator set of points. We prove that the higgledy-piggledy set of -subspaces has to contain elements. We also prove that has to contain elements if the field is algebraically closed. An -uniform (, ) subspace design is a set of linear subspaces each of rank such that each linear subspace of rank meets at most among them. This subspace design is an -uniform (, ) subspace design if for of rank . We prove that if then the dual () of an -uniform weak (strong) subspace design of parameter (, ) is an -uniform weak (strong) subspace design of parameter (, ). We show the connection between uniform weak subspace designs and higgledy-piggledy subspaces proving that for -uniform weak or strong (, ) subspace designs in . We show that the -uniform strong subspace design constructed by Guruswami and Kopparty (based on multiplicity codes) has parameter if we consider it as a subspace design. We give some similar constructions of weak and strong subspace designs (and higgledy-piggledy subspaces) and prove that the lower bound over algebraically closed field is tight. |
Year | DOI | Venue |
|---|---|---|
2016 | https://doi.org/10.1007/s10623-016-0189-4 | Designs, Codes and Cryptography |
Keywords | Field | DocType |
Projective space,Subspace design,General position,05B25,51E20,51D20 | Discrete mathematics,General position,Combinatorics,Subspace topology,Upper and lower bounds,Multiplicity (mathematics),Linear subspace,Mathematics,Algebraically closed field,Projective space | Journal |
Volume | Issue | Citations |
79 | 3 | 0 |
PageRank | References | Authors |
0.34 | 3 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Szabolcs L. Fancsali | 1 | 9 | 2.32 |
| Peter Sziklai | 2 | 41 | 6.94 |