Table of Contents

PART I: Basic Coding Theory1. Introduction2. Block Codes, Weight, and Distance3. Linear Codes4. Error Processing for Linear Codes5. Hamming Codes and the Binary Golay CodesPART II: Finite Fields6. Introduction7. Euclid's Algorithm8. Invertible and Irreducible Elements9. The Construction of Finite Fields10. The Structure of Finite Fields11. Roots of Polynomials12. Primitive ElementsPART III: BCH and Other Cyclic Codes13. BCH Codes as Subcodes of Hamming Codes14. BCH Codes as Polynomial Codes15. Decoding BCH Codes: The Fundamental Equation16. Decoding BCH Codes: A Decoding Algorithm17. Reed-Solomon Codes and Burst Error Correction18. Bounds on CodesPART IV: Classical and Geometric Goppa Codes19. Classical Goppa Codes20. Classical Goppa Codes: Error Processing21. Introduction to Algebraic Curves22. Functions on Algebraic Curves23. A Survey of the Theory of Algebraic Curves24. Geometric Goppa Codes25. An Error Processor for Geometric Goppa Codes