Name
Abstract | ||
|---|---|---|
Let Aq(n, d, k) denote the maximum cardinality of a set C of k-dimensional subspaces of an n-dimensional vector space over the finite field of order q, F q, such that any two different subspaces U, W. C have a distance d(U, W) := dim(U + W) -dim(U n W) of at least d. Lower bounds on Aq(n, d, k) can be obtained by explicitly constructing corresponding sets C. When searching for such sets with a prescribed group of automorphisms, the search problem leads to instances of the maximum weight clique problem. The main focus is here on subgroups with small index in the normalizer of a Singer subgroup of GL(n, q). With a stochastic maximum weight clique algorithm and a systematic consideration of groups of the above mentioned type, new lower bounds on A2(8, 4, 4) and A2(n, 4, 3) for 8 = n = 11 are obtained. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1080/10586458.2016.1239145 | EXPERIMENTAL MATHEMATICS |
Keywords | Field | DocType |
constant-dimension codes,integer linear programming,packing,random network coding | Mathematical analysis,Cardinality,Clique problem,Discrete mathematics,Topology,Vector space,Finite field,Combinatorics,Clique,Automorphism,Linear subspace,Centralizer and normalizer,Mathematics | Journal |
Volume | Issue | ISSN |
27.0 | 2.0 | 1058-6458 |
Citations | PageRank | References |
1 | 0.36 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Braun | 1 | 132 | 19.64 |
| Patric R. J. Östergård | 2 | 609 | 70.61 |
| Alfred Wassermann | 3 | 125 | 23.33 |