Tables of subspace codes

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Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Tables of subspace codes.
Bayreuth , 2019 . - 44 S.

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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 the n-dimensional vector space of the finite field with q elements, where the dimensions of the codewords, which are vector spaces, are contained in {0,1,...,n}. In the special case of K={k} one speaks of constant dimension codes. Since this (still) emerging field is 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 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.