407 research outputs found
On conjugacy classes of subgroups of the general linear group and cyclic orbit codes
Orbit codes are a family of codes employable for communications on a random
linear network coding channel. The paper focuses on the classification of these
codes. We start by classifying the conjugacy classes of cyclic subgroups of the
general linear group. As a result, we are able to focus the study of cyclic
orbit codes to a restricted family of them.Comment: 5 pages; Submitted to IEEE International Symposium on Information
Theory (ISIT) 201
Cyclic Orbit Codes
In network coding a constant dimension code consists of a set of
k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes
which are defined as orbits of a subgroup of the general linear group, acting
on the set of all subspaces of F_q^n. If the acting group is cyclic, the
corresponding orbit codes are called cyclic orbit codes. In this paper we give
a classification of cyclic orbit codes and propose a decoding procedure for a
particular subclass of cyclic orbit codes.Comment: submitted to IEEE Transactions on Information Theor
A subspace code of size 333 in the setting of a binary q-analog of the Fano plane
We show that there is a binary subspace code of constant dimension 3 in
ambient dimension 7, having minimum distance 4 and cardinality 333, i.e., , which improves the previous best known lower bound of 329.
Moreover, if a code with these parameters has at least 333 elements, its
automorphism group is in one of conjugacy classes. This is achieved by a
more general technique for an exhaustive search in a finite group that does not
depend on the enumeration of all subgroups.Comment: 18 pages; typos correcte
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