7 research outputs found
Subspaces intersecting in at most a point
We improve on the lower bound of the maximum number of planes in
\operatorname{PG}(8,q)\cong\F_q^{9} pairwise intersecting in at most a point.
In terms of constant dimension codes this leads to . This result is obtained via a more general
construction strategy, which also yields other improvements.Comment: 4 page
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
The interplay of different metrics for the construction of constant dimension codes
A basic problem for constant dimension codes is to determine the maximum
possible size of a set of -dimensional subspaces in
, called codewords, such that the subspace distance satisfies
for all pairs of different codewords ,
. Constant dimension codes have applications in e.g.\ random linear network
coding, cryptography, and distributed storage. Bounds for are the
topic of many recent research papers. Providing a general framework we survey
many of the latest constructions and show up the potential for further
improvements. As examples we give improved constructions for the cases
, , , and . We also derive
general upper bounds for subcodes arising in those constructions.Comment: 19 pages; typos correcte