Parallel versions of the linkage construction and of multi-block lifted MRD codes yield new lower bounds on A_q(n,d,k), beating the previous tables in more than 110 cases.
Large Sets of $t$-Designs over Finite Fields
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abstract
A $t\text{-}(n,k,\lambda;q)$-design is a set of $k$-subspaces, called blocks, of an $n$-dimensional vector space $V$ over the finite field with $q$ elements such that each $t$-subspace is contained in exactly $\lambda$ blocks. A partition of the complete set of $k$-subspaces of $V$ into disjoint $t\text{-}(n,k,\lambda;q)$ 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 $t\ge2$.
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cs.IT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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New Constructions of Subspace Codes Using Subsets of MRD codes in Several Blocks
Parallel versions of the linkage construction and of multi-block lifted MRD codes yield new lower bounds on A_q(n,d,k), beating the previous tables in more than 110 cases.