Abstract A 2-(v, k, λ) design is additive (or strongly additive) if it is possible to embed it in a
suitable abelian group G in such a way that its block set is contained in (or coincides with) …

Combinatorial designs have been studied for nearly 200 years. 50 years ago, Cameron,
Delsarte, and Ray-Chaudhury started investigating their q-analogs, also known as subspace …

Abstract The Assmus-Mattson Theorem gives a way to identify block designs arising from
codes. This result was broadened to matroids and weighted designs by Britz et al. in 2009 …

We investigate two fundamental questions intersecting coding theory and combinatorial
geometry, with emphasis on their connections. These are the problem of computing the …

We investigate the existence of Boolean degree $ d $ functions on the Grassmann graph of
$ k $-spaces in the vector space $\mathbb {F} _q^ n $. For $ d= 1$ several non-existence …

A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same
size. In this paper we introduce the q-analogue of a PMD and its properties. In order to do …

Grassmannian G _q (n, k) G q (n, k) is the set of all k-dimensional subspaces of the vector
space F _q^ n F qn. Kötter and Kschischang showed that codes in Grassmannian space can …

Let PG (F qv) be the (v− 1)‐dimensional projective space over F q and let Γ be a simple
graph of order qk− 1 q− 1 for some k. A 2−(v, Γ, λ) design over F q is a collection ℬ of graphs …

arxiv:1808.03580v3 [math.CO] 16 Jan 2019 Page 1 JOHNSON TYPE BOUNDS FOR MIXED
DIMENSION SUBSPACE CODES THOMAS HONOLD, MICHAEL KIERMAIER, AND SASCHA …

We give new constructions of two classes of algebraic code families that are efficiently list
decodable with small output list size from a fraction 1-R-ε of adversarial errors, where R is …