Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655289 | Journal of Combinatorial Theory, Series A | 2014 | 12 Pages |
Abstract
A t-(n,k,λ)t-(n,k,λ) design over FqFq is a collection of k -dimensional subspaces of Fqn, called blocks, such that each t -dimensional subspace of Fqn is contained in exactly λ blocks. Such t -designs over FqFq are the q -analogs of conventional combinatorial designs. Nontrivial t-(n,k,λ)t-(n,k,λ) designs over FqFq are currently known to exist only for t⩽3t⩽3. Herein, we prove that simple (meaning, without repeated blocks) nontrivial t-(n,k,λ)t-(n,k,λ) designs over FqFq exist for all t and q , provided that k>12(t+1)k>12(t+1) and n is sufficiently large. This may be regarded as a q-analog of the celebrated Teirlinck theorem for combinatorial designs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Arman Fazeli, Shachar Lovett, Alexander Vardy,