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2003 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Block Error-Correcting Codes

A Computational Primer

verfasst von: Sebastià Xambó-Descamps

Verlag: Springer Berlin Heidelberg

Buchreihe : Universitext

Enthalten in: Professional Book Archive

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Über dieses Buch

Error-correcting codes have been incorporated in numerous working communication and memory systems. This book covers the mathematical aspects of the theory of block error-correcting codes together, in mutual reinforcement, with computational discussions, implementations and examples of all relevant concepts, functions and algorithms. This combined approach facilitates the reading and understanding of the subject.

The digital companion of the book is a non-printable .pdf document with hyperlinks. The examples included in the book can be run with just a mouse click and modified and saved by users for their own purpose.

Inhaltsverzeichnis

Frontmatter
Introduction
Abstract
This chapter is meant to be an informal introduction to the main ideas of error-correcting block codes.
Sebastià Xambó-Descamps
1. Block Error-correcting Codes
Abstract
The goal of this chapter is the study of some basic concepts and constructions pertaining to block error-correcting codes, and of their more salient properties, with a strong emphasis on all the relevant algorithmic and computational aspects.
Sebastià Xambó-Descamps
2. Finite Fields
Abstract
This chapter is devoted to the presentation of some of the basic ideas and results of the theory of finite fields that are used in the theory of error-correcting codes. It is a self-contained exposition, up to a few elementary ideas on rings and polynomials (for the convenience of the reader, the latter are summarized below). On the computational side, we include a good deal of details and examples of how finite fields and related objects can be constructed and used.
Sebastià Xambó-Descamps
3. Cyclic Codes
Abstract
Cyclic codes are linear codes that are invariant under cyclic permutations of the components of its vectors. These codes have a nice algebraic structure (after reinterpreting vectors as univariate polynomials) which favors its study and use in a particularly effective way.
Sebastià Xambó-Descamps
4. Alternant Codes
Abstract
In this chapter we will introduce the class of alternant codes over F q by means of a (generalized) control matrix. This matrix looks like the control matrix of a general Reed-Solomon code (Example 1.26), but it is defined over an extension F q m of F q and the h i need not be related to the αi. Lower bounds for the minimum distance and the dimension follow easily from the definition. In fact these bounds generalize the corresponding lower bounds for BCH codes and the proofs are similar.
Sebastià Xambó-Descamps
Backmatter
Metadaten
Titel
Block Error-Correcting Codes
verfasst von
Sebastià Xambó-Descamps
Copyright-Jahr
2003
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-18997-5
Print ISBN
978-3-540-00395-3
DOI
https://doi.org/10.1007/978-3-642-18997-5