1,121 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
Geometry of the inversion in a finite field and partitions of in normal rational curves
Let be a finite field and let be a
subfield of .
Consider as a vector space over and the associated projective space
that is isomorphic to .
The properties of the projective mapping induced by have
been studied in \cite{Cs13,Fa02,Ha83,He85,Bu95}, where it is proved that the
image of any line is a normal rational curve in some subspace.
In this note a more detailed geometric description is achieved.
Consequences are found related to mixed partitions of the projective spaces;
in particular, it is proved that for any positive integer , if ,
then there are partitions of in normal rational curves
of degree .
For smaller the same construction gives partitions in -tuples of
independent points
Quanta Without Quantization
The dimensional properties of fields in classical general relativity lead to
a tangent tower structure which gives rise directly to quantum mechanical and
quantum field theory structures without quantization. We derive all of the
fundamental elements of quantum mechanics from the tangent tower structure,
including fundamental commutation relations, a Hilbert space of pure and mixed
states, measurable expectation values, Schroedinger time evolution, collapse of
a state and the probability interpretation. The most central elements of string
theory also follow, including an operator valued mode expansion like that in
string theory as well as the Virasoro algebra with central charges.Comment: 8 pages, Latex, Honorable Mention 1997 GRG Essa
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
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