Large sets of subspace designs

Abstract

In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Graßmannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to subspace designs. We construct a $2$-$(6,3,78{)}_5$ design by computer, which corresponds to a halving ${\mathrm{LS}}_5[2](2,3,6)$. The application of the new recursion method to this halving and an already known ${\mathrm{LS}}_3[2](2,3,6)$ yields two infinite two-parameter series of halvings ${\mathrm{LS}}_3[2](2,k,v)$ and ${\mathrm{LS}}_5[2](2,k,v)$ with integers $v\ge 6$, $v\equiv 2\mathrm{mod}4$ and $3\le k\le v-3$, $k\equiv 3\mathrm{mod}4$. Thus in particular, two new infinite series of nontrivial subspace designs with $t=2$ are constructed. Furthermore as a corollary, we get the existence of infinitely many nontrivial large sets of subspace designs with $t=2$.

References in corpus (5)

• Optimal Binary Subspace Codes of Length 6, Constant Dimension 3 and Minimum Distance 4
• To the theory of $q$-ary Steiner and other-type trades
• Intersection numbers for subspace designs
• Derived and Residual Subspace Designs
• The minimum volume of subspace trades

Cited by in corpus (8)

• To the theory of $q$-ary Steiner and other-type trades
• The order of the automorphism group of a binary $q$-analog of the Fano plane is at most two
• On the automorphism group of a binary $q$-analog of the Fano plane
• Subspace Packings -- Constructions and Bounds
• A new series of large sets of subspace designs over the binary field
• The minimum volume of subspace trades
• Constructions of new matroids and designs over GF(q)
• On $\alpha$-points of $q$-analogs of the Fano plane