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Tables of subspace codes

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arxiv 1601.02864 v3 pith:DN7UZJGS submitted 2016-01-12 math.CO cs.ITmath.IT

Daniel Heinlein , Michael Kiermaier , Sascha Kurz , Alfred Wassermann This is my paper · ORCID
classification math.COcs.ITmath.IT
keywords subspacecodesimplementedknowledgeleasttechnicalalgorithmicasks
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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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Cited by 3 Pith papers

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  1. Asymptotically optimal cyclic subspace codes

    cs.IT 2025-07 conditional novelty 8.0 of 10

    A nesting operation builds cyclic subspace codes with minimum distance 2k-2 whose size asymptotically matches the Johnson bound when n/k is a power of 3.

  2. Combinatorial constructions of Schubert subspace codes

    math.CO 2026-07 accept novelty 6.0 of 10

    Two constructions of optimal Schubert subspace codes are given: one via direct-sum decomposition with partial spreads and q-Johnson graph colorings, another via field reduction from scattered subspaces, recovering the...

  3. Generalized bilateral multilevel construction for constant dimension codes from parallel mixed dimension construction

    cs.IT 2025-07 conditional novelty 5.0 of 10

    New lower bounds for constant dimension codes A_q(n,2δ,{k}) are obtained by adding a generalized bilateral multilevel construction onto the parallel mixed dimension construction.

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