10 research outputs found
Subspace code constructions
We improve on the lower bound of the maximum number of planes of mutually intersecting in at most one point leading to the following
lower bound: for
constant dimension subspace codes. We also construct two new non-equivalent
constant dimension subspace orbit-codes
Tables of subspace codes
One of the main problems of subspace coding asks for the maximum possible
cardinality of a subspace code with minimum distance at least over
, where the dimensions of the codewords, which are vector
spaces, are contained in . In the special case of
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.Comment: 44 pages, 6 tables, 7 screenshot
Combining subspace codes
In the context of constant--dimension subspace codes, an important problem is
to determine the largest possible size of codes whose codewords
are -subspaces of with minimum subspace distance . Here
in order to obtain improved constructions, we investigate several approaches to
combine subspace codes. This allow us to present improvements on the lower
bounds for constant--dimension subspace codes for many parameters, including
, , and .Comment: 17 pages; construction for A_(10,4;5) was flawe
ORBIT CODES FROM FORMS ON VECTOR SPACES OVER A FINITE FIELD
In this paper we construct different families of orbit codes in the vector spaces of the symmetric bilinear forms, quadratic forms and Hermitian forms on an n-dimensional vector space over the finite field Fq. All these codes admit the general linear group GL(n, q) as a transitive automorphism group
Veronese subspace codes
Using the correspondence between quadrics of and points of
, a family of
constant dimension subspace codes is constructed