Coding theory has grown into a discipline with many practical applications requiring various mathematical techniques in the last few decades. Most topics covered in this book are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references.

Part I. Coding Fundamentals. 1. Basics of Coding Theory. 2. Cyclic Codes over Finite Fields. 3. Construction and Classification of Codes. 4. Self-Dual Codes. 5. Codes and Designs. 6. Codes over Rings. 7. Quasi-Cyclic Codes. 8. Introduction to Skew-Polynomial Rings and Skew-Cyclic Codes. 9. Additive Cyclic Codes. 10. Convolutional Codes. 11. Rank-Metric Codes. 12. Linear Programming Bounds. 13. Semidefinite Programming Bounds for Error-Correcting Codes. Part II. Families of Codes. 14. Coding Theory and Galois Geometries. 15. Algebraic Geometry Codes and Some Applications. 16. Codes in Group Algebras. 17. Constacyclic Codes over Finite Commutative Chain Rings. 18. Weight Distribution of Trace Codes over Finite Rings. 19. Two-Weight Codes. 20. Linear Codes from Functions. 21. Codes over Graphs. Part III. Applications. 22. Alternative Metrics. 23. Algorithmic Methods. 24. Interpolation Decoding. 25. Pseudo-Noise Sequences. 26. Lattice Coding. 27. Quantum Error-Control Codes. 28. Space-Time Coding. 29. Network Codes. 30. Coding for Erasures and Fountain Codes. 31. Codes for Distributed Storage. 32. Polar Codes. 33. Secret Sharing with Linear Codes. 34. Code-Based Cryptography. Bibliography. Index.