Computation of the weight distribution of CRC codes

In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from some "representative” words. Thanks to MacWilliams' Theorem, the computation of the weight distribution of the dual codes can be easily brought back to that of CRC code

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

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

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

Calcolo della Distribuzione dei Pesi nei Codici Ciclici Accorciati

La tesi parte dall'algoritmo sul calcolo della distribuzione dei pesi per codici CRC che si trova nell'articolo di Castagnoli-Bräuer-Hermann dal titolo "Optimization of Cyclic Redundancy-Check Codes with 24 and 32 Parity Bits" pubblicata dalla IEEE Trans. on Communication nel giugno del 1993. Lo scopo della tesi è l'estensione di tale algoritmo ai campi finiti con p^n elementi con p un primo. Per lo sviluppo di tale algoritmo si sono toccati argomenti di algebra di base e sono stati dimostrati risultati sulla scomposizione di quozienti dell'anello dei polinomi sul campo con p^n elementi. La tesi comprende pure una implementazione dell'algoritmo nel caso p=2 e n=1 in linguaggio C++ con la libreria NTL (number theory library)