Table of contents for Error-correcting codes and finite fields / Oliver Pretzel.


Bibliographic record and links to related information available from the Library of Congress catalog


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PART I: Basic Coding Theory


1. Introduction


2. Block Codes, Weight, and Distance


3. Linear Codes


4. Error Processing for Linear Codes


5. Hamming Codes and the Binary Golay Codes


PART II: Finite Fields


6. Introduction


7. Euclid's Algorithm


8. Invertible and Irreducible Elements


9. The Construction of Finite Fields


10. The Structure of Finite Fields


11. Roots of Polynomials


12. Primitive Elements


PART III: BCH and Other Cyclic Codes


13. BCH Codes as Subcodes of Hamming Codes


14. BCH Codes as Polynomial Codes


15. Decoding BCH Codes: The Fundamental Equation


16. Decoding BCH Codes: A Decoding Algorithm


17. Reed-Solomon Codes and Burst Error Correction


18. Bounds on Codes


PART IV: Classical and Geometric Goppa Codes


19. Classical Goppa Codes


20. Classical Goppa Codes: Error Processing


21. Introduction to Algebraic Curves


22. Functions on Algebraic Curves


23. A Survey of the Theory of Algebraic Curves


24. Geometric Goppa Codes


25. An Error Processor for Geometric Goppa Codes





Library of Congress subject headings for this publication:
Error-correcting codes (Information theory)