Librería Portfolio

Features

Offers comprehensive coverage of coding theory
Includes a new part on algebraic curves and important applications to coding theory
Provides a new chapter on linear programming
Contains tables on small fields and parameters of codes
Adds material on finite fields
Summary

This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.



Table of Contents

An Elementary Introduction to Coding. The Concept of Coding. Binary Linear Codes. General Linear Codes. Reed-Solomon Codes. Recursive Construction I. Universal Hashing. Designs and the Binary Golay Code. Shannon Entropy. Asymptotic Results. 3-Dimensional Codes, Projective Planes. Summary and Outlook. The Theory of Codes and Their Applications. Subfield Codes and Trace Codes. Cyclic Codes. Recursive Constructions, Covering Radius. OA in Statistics and Computer Science. The Geometric Description of Codes. Additive Codes. Algebraic Curves. Introduction. Applications to Coding Theory.