A First Course in Coding Theory


1. Introduction to error-correcting codes
2. The main coding theory problem
3. An introduction to finite fields
4. Vector spaces over finite fields
5. Introduction to linear codes
6. Encoding and decoding with a linear code
7. The dual code, the parity check matrix, and syndrome decoding
8. The Hamming codes
9. Perfect codes
10. Codes and Latin squares
11. A double-error correcting decimal code and an introduction to BCH codes
12. Cyclic codes
13. Weight enumerators
14. The main linear coding theor problem
15. MDS codes
16. Concluding remarks, related topics, and further reading
Solutions to exercises