The Mathematics of Coding Theory

Designed for undergraduate courses in coding theory and network security, in departments of mathematics, electrical engineering, and computer science, this text is an accessible introduction to important contemporary applications of number theory, abstract algebra and probability. 1. Probability -- 2. Information -- 3. Noiseless Coding -- 4. Noisy Coding -- 5. Cyclic Redundancy Checks -- 6. The Integers -- 7. Permutations and Interleavers -- 8. Groups -- 9. Rings and Fields -- 10. Polynomials -- 11. Finite Fields -- 12. Linear Codes -- 13. Bounds for Codes -- 14. More on Linear Codes -- 15. Primitive Roots -- 16. Primitive Polynomials -- 17. RS and BCH Codes -- 18. Concatenated Codes -- 19. More on Rings and Fields -- 20. Curves and Codes -- App. Stirling's Formula -- App. Polynomials