Lecture plan (final)
Chapters are from the book Fundamentals of Error-Correcting Codes.
| Week | Topic | Key words | Chapters |
|---|---|---|---|
| 2 | Introduction - Linear codes | Generator & parity check matrices. | 1.1–1.2. |
| 3 | Linear codes (ctd.) | Equivalence of codes, weight, distance, encoding & decoding. | 1.6, 1.4, 1.11. |
| 4 | Linear codes (ctd.) | Syndrome decoding, Shannon's theorem, sphere packing, Hamming codes & perfect codes. | 1.8, 1.11–1.12. |
| 5 | Linear codes (ctd.) | Code modification & dual codes. | 1.3, 1.5. |
| 6 | Linear codes (ctd.) | Reed–Muller codes. | 1.10, 13.2.3. |
| 7 | Code size bounds - Finite fields | MDS codes, introduction & irreducible polynomials. | 2.1, 2.4, 2.8, 3.1–3.2. |
| 8 | Finite fields - Cyclic codes | Construction, primitive elements, generating polynomials. | 3.3–3.7, 4.2. |
| 9 | Cyclic codes (ctd.) | Factorisation of \(x^n-1\), idempotents. | 4.1, 4.3. |
| 10 | Cyclic codes (ctd.) | Zeroes & minimum distance (BCH-bound) | 4.4–4.5. |
| 11 | BCH codes | Designed distance, dimension | 5.1. |
| 12 | BCH codes (ctd.) | Reed–Solomon codes | 5.2. |
| 13 | Cancelled Lectures | ||
| 14 | Easter Break | ||
| 15 | BCH codes (ctd.) | Decoding, Berlekamp–Massey. | 5.4.2. |
| 16 | Convolutional codes | Encoding, state & trellis diagrams & Viterbi decoding | 14.1–14.5. |
| 17 | Recap | ||
| 22 | Exam | All of the above. | |