Tables of subspace codes

TL;DR

This paper introduces an online database for subspace codes, summarizing current theoretical and algorithmic knowledge, to aid researchers in understanding and advancing the field of subspace coding.

Contribution

It provides a comprehensive, regularly updated online database of subspace code results and offers a user guide for leveraging this resource in research.

Findings

Development of an online database of subspace codes

Compilation of theoretical and algorithmic results in the field

Facilitation of research and knowledge sharing in subspace coding

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.