Jorunal of Combinatorial Theory 124

Large Sets of t-Design over Finite Fields
Alfred Wassermann ; Michael Braun; Axel Kohnert; Patric R.J. Östergård

2014, Elsevier, in: Journal of Combinatorial Theorie, Series A, Jg.:2014, Hnr.: 124, S.: 195  - 201 Doi-Nummer: 10.1016/j.jcta.2014.01.008

Abstract:
A t-(n,k,λ;q)t-(n,k,λ;q)-design is a set of k -dimensional subspaces, called blocks, of an n -dimensional vector space V over the finite field with q elements such that each t -dimensional subspace is contained in exactly λ blocks. A partition of the complete set of k -dimensional subspaces of V into disjoint t-(n,k,λ;q)t-(n,k,λ;q) designs is called a large set of t -designs over finite fields. In this paper we give the first nontrivial construction of such a large set with t⩾2t⩾2.

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