Felice Manganiello

Spread codes and spread decoding in network coding

In this paper we introduce the class of spread codes for the use in random network coding. Spread codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding algorithm of spread codes up to half the minimum distance.

Cyclic Orbit Codes

A constant dimension code consists of a set of k-dimensional subspaces of \BBF qn. 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 \BBF qn. If the acting group is cyclic, the corresponding orbit codes are called cyclic orbit codes. In this paper, we show how orbit codes can be seen as an analog of linear codes in the block coding case. We investigate how the structure of cyclic orbit codes can be utilized to compute the minimum distance and cardinality of a given code and propose different decoding procedures for a particular subclass of cyclic orbit codes.

Orbit codes — A new concept in the area of network coding

We introduce a new class of constant dimension codes called orbit codes. The basic properties of these codes are derived. It will be shown that many of the known families of constant dimension codes in the literature are actually orbit codes.

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

On conjugacy classes of subgroups of the general linear group and cyclic orbit codes

k\times n

Kötter interpolation in skew polynomial rings

with entries in a finite field

Construction and decoding of generalized skew-evaluation codes

\mathbb F_q

Matroidal structure of skew polynomial rings with application to network coding

. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires

Computation of the weight distribution of CRC codes

\mathcal{O}((n-k)k^3)

Representations of the Multicast Network Problem

operations over an extension field