Error-Correcting Codes and Finite Fields

Name: Error-Correcting Codes and Finite Fields
Price: 6.75 USD
Availability: InStock
ISBN: 9780192690678

ISBN-10: 0192690671

ISBN-13: 9780192690678

Edition: 1996 (Student Manual, Study Guide, etc.)

Authors: Oliver Pretzel

List price: $90.00

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This book provides engineers and computer scientists with all the tools necessary to implement modern error-processing techniques. It assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples which motivate and explain the theory. The first part introduces the basic ideas of coding theory. The second and third cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. The fourth part is devoted to Goppa codes, both classical and geometric, concluding with the Skorobogatov-Vladut error processor. A special feature is a simplified (but rigorous) treatment of the…

Book details

List price: $90.00
Copyright year: 1996
Publisher: Oxford University Press, Incorporated
Publication date: 8/29/1996
Binding: Paperback
Pages: 356
Size: 6.14" wide x 9.21" long x 0.75" tall
Weight: 1.144
Language: English




Basic Coding Theory



Introduction



Block Codes, Weight, and Distance



Linear Codes



Error Processing for Linear Codes



Hamming Codes and the Binary Golay Codes



Finite Fields



Introduction



Euclid's Algorithm



Invertible and Irreducible Elements



The Construction of Finite Fields



The Structure of Finite Fields



Roots of Polynomials



Primitive Elements



BCH and Other Cyclic Codes



BCH Codes as Subcodes of Hamming Codes



BCH Codes as Polynomial Codes



Decoding BCH Codes: The Fundamental Equation



Decoding BCH Codes: A Decoding Algorithm



Reed-Solomon Codes and Burst Error Correction



Bounds on Codes



Classical and Geometric Goppa Codes



Classical Goppa Codes



Classical Goppa Codes: Error Processing



Introduction to Algebraic Curves



Functions on Algebraic Curves



A Survey of the Theory of Algebraic Curves



Geometric Goppa Codes



An Error Processor for Geometric Goppa Codes