English

Tables of subspace codes

Combinatorics 2019-12-24 v3 Information Theory math.IT

Abstract

One of the main problems of subspace coding asks for the maximum possible cardinality of a subspace code with minimum distance at least dd over Fqn\mathbb{F}_q^n, where the dimensions of the codewords, which are vector spaces, are contained in K{0,1,,n}K\subseteq\{0,1,\dots,n\}. In the special case of K={k}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.

Keywords

Cite

@article{arxiv.1601.02864,
  title  = {Tables of subspace codes},
  author = {Daniel Heinlein and Michael Kiermaier and Sascha Kurz and Alfred Wassermann},
  journal= {arXiv preprint arXiv:1601.02864},
  year   = {2019}
}

Comments

44 pages, 6 tables, 7 screenshots

R2 v1 2026-06-22T12:27:48.226Z