Optimal Schubert subspace codes of size A_q(u,ℓ,2(ℓ−t)) are constructed via direct-sum partial spreads with q-Johnson colorings and via field reduction of h-scattered subspaces.
Tables of subspace codes
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abstract
One of the main problems of subspace coding asks for the maximum possible cardinality of a subspace code with minimum distance at least $d$ over $\mathbb{F}_q^n$, where the dimensions of the codewords, which are vector spaces, are contained in $K\subseteq\{0,1,\dots,n\}$. In the special case of $K=\{k\}$ one speaks of constant dimension codes. Since this (still) emerging field is very prosperous on the one hand side and there are a lot of connections to classical objects from Galois geometry it is a bit difficult to keep or to obtain an overview about the current state of knowledge. To this end we have implemented an on-line database of the (at least to us) known results at \url{subspacecodes.uni-bayreuth.de}. The aim of this recurrently updated technical report is to provide a user guide how this technical tool can be used in research projects and to describe the so far implemented theoretic and algorithmic knowledge.
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Combinatorial constructions of Schubert subspace codes
Optimal Schubert subspace codes of size A_q(u,ℓ,2(ℓ−t)) are constructed via direct-sum partial spreads with q-Johnson colorings and via field reduction of h-scattered subspaces.