A new series of large sets of subspace designs over the binary field
| Autor: | Alfred Wassermann, Michael Kiermaier, Reinhard Laue |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Applied Mathematics Modulo 010102 general mathematics 0102 computer and information sciences Disjoint sets 01 natural sciences Linear subspace Computer Science Applications Binary fields Combinatorics 010201 computation theory & mathematics FOS: Mathematics Partition (number theory) Mathematics - Combinatorics Combinatorics (math.CO) 0101 mathematics Recursion method Subspace topology Mathematics Vector space |
| Popis: | In this article, we show the existence of large sets $${\text {LS}}_2[3](2,k,v)$$ for infinitely many values of k and v. The exact condition is $$v \ge 8$$ and $$0 \le k \le v$$ such that for the remainders $$\bar{v}$$ and $$\bar{k}$$ of v and k modulo 6 we have $$2 \le \bar{v} < \bar{k} \le 5$$ . The proof is constructive and consists of two parts. First, we give a computer construction for an $${\text {LS}}_2[3](2,4,8)$$ , which is a partition of the set of all 4-dimensional subspaces of an 8-dimensional vector space over the binary field into three disjoint 2- $$(8, 4, 217)_2$$ subspace designs. Together with the already known $${\text {LS}}_2[3](2,3,8)$$ , the application of a recursion method based on a decomposition of the Grasmannian into joins yields a construction for the claimed large sets. |
| Databáze: | OpenAIRE |
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