Tables of subspace codes

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.

44 pages, 6 tables, 7 screenshots

References in corpus (10)

• Coset Construction for Subspace Codes
• Partial spreads and vector space partitions
• The order of the automorphism group of a binary $q$-analog of the Fano plane is at most two
• Projective divisible binary codes
• Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects
• A New Approach to the Main Problem of Subspace Coding
• The Expurgation-Augmentation Method for Constructing Good Plane Subspace Codes
• Upper bounds for partial spreads
• Some constructions of cyclic and quasi-cyclic subspaces codes
• Optimal Binary $(5,3)$ Projective Space Codes from Maximal Partial Spreads

Cited by in corpus (23)

• Coset Construction for Subspace Codes
• Partial spreads and vector space partitions
• Combining subspace codes
• A note on the linkage construction for constant dimension codes
• Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects
• The Expurgation-Augmentation Method for Constructing Good Plane Subspace Codes
• Parameter-controlled inserting constructions of constant dimension subspace codes
• Upper bounds for partial spreads
• New LMRD bounds for constant dimension codes and improved constructions
• Parallel multilevel constructions for constant dimension codes
• Constructions and Bounds for Mixed-Dimension Subspace Codes
• Explicit Good Subspace-metric Codes and Subset-metric Codes
• Generalized vector space partitions
• Construction of Const Dimension Codes from Serval Parallel Lift MRD Code
• On projective $q^r$-divisible codes
• New Constructions of Subspace Codes Using Subsets of MRD codes in Several Blocks
• Construction of Const Dimension Code from Two Parallel Versions of Linkage Construction
• Johnson type bounds for mixed dimension subspace codes
• Intersection Patterns in Optimal Binary $(5,3)$ Doubling Subspace Codes
• New and Updated Semidefinite Programming Bounds for Subspace Codes
• Several classes of optimal Ferrers diagram rank-metric codes
• Abelian Noncyclic Orbit Codes and Multishot Subspace Codes
• Designs and codes in affine geometry