2018/06/01 by Byrne, Eimear, Ravagnani, Alberto
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1806.00448
A t-(n,d,λ) design over \mathbb Fq, or a subspace design, is a collection of d-dimensional subspaces of \mathbb Fqn, called blocks, with the property that every t-dimensional subspace of \mathbb Fqn is contained in the same number λ of blocks. A collection of matrices in over \mathbb Fq is said to hold a subspace design if the set of column spaces of its elements forms the blocks of a subspace design. We use notions of puncturing and shortening of rank metric codes and the rank-metric MacWilliams identities to establish conditions under which the words of a given rank in a linear rank metric code hold a subspace design.