13 research outputs found
An Algebraic Approach for Decoding Spread Codes
In this paper we study spread codes: a family of constant-dimension codes for
random linear network coding. In other words, the codewords are full-rank
matrices of size (k x n) with entries in a finite field F_q. Spread codes are a
family of optimal codes with maximal minimum distance. We give a
minimum-distance decoding algorithm which requires O((n-k)k^3) operations over
an extension field F_{q^k}. Our algorithm is more efficient than the previous
ones in the literature, when the dimension k of the codewords is small with
respect to n. The decoding algorithm takes advantage of the algebraic structure
of the code, and it uses original results on minors of a matrix and on the
factorization of polynomials over finite fields
Message Encoding for Spread and Orbit Codes
Spread codes and orbit codes are special families of constant dimension
subspace codes. These codes have been well-studied for their error correction
capability and transmission rate, but the question of how to encode messages
has not been investigated. In this work we show how the message space can be
chosen for a given code and how message en- and decoding can be done.Comment: Submitted to IEEE International Symposium on Information Theory 201
Isometry and Automorphisms of Constant Dimension Codes
We define linear and semilinear isometry for general subspace codes, used for
random network coding. Furthermore, some results on isometry classes and
automorphism groups of known constant dimension code constructions are derived
Partial Spreads in Random Network Coding
Following the approach by R. K\"otter and F. R. Kschischang, we study network
codes as families of k-dimensional linear subspaces of a vector space F_q^n, q
being a prime power and F_q the finite field with q elements. In particular,
following an idea in finite projective geometry, we introduce a class of
network codes which we call "partial spread codes". Partial spread codes
naturally generalize spread codes. In this paper we provide an easy description
of such codes in terms of matrices, discuss their maximality, and provide an
efficient decoding algorithm
Spread Decoding in Extension Fields
A spread code is a set of vector spaces of a fixed dimension over a finite
field Fq with certain properties used for random network coding. It can be
constructed in different ways which lead to different decoding algorithms. In
this work we present a new representation of spread codes with a minimum
distance decoding algorithm which is efficient when the codewords, the received
space and the error space have small dimension.Comment: Submitted for publication to Finite Fields and their Applications
(Elsevier
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