# Lecture plan (final)

Chapters are from the book Fundamentals of Error-Correcting Codes.

WeekTopicKey wordsChapters
2Introduction - Linear codesGenerator & parity check matrices.1.1–1.2.
3Linear codes (ctd.) Equivalence of codes, weight, distance, encoding & decoding.1.6, 1.4, 1.11.
4Linear codes (ctd.) Syndrome decoding, Shannon's theorem, sphere packing,
Hamming codes & perfect codes.
1.8, 1.11–1.12.
5Linear codes (ctd.) Code modification & dual codes.1.3, 1.5.
6Linear codes (ctd.) Reed–Muller codes.1.10, 13.2.3.
7Code size bounds -
Finite fields
MDS codes,
introduction & irreducible polynomials.
2.1, 2.4, 2.8,
3.1–3.2.
8Finite fields -
Cyclic codes
Construction, primitive elements,
generating polynomials.
3.3–3.7,
4.2.
9Cyclic codes (ctd.)Factorisation of $x^n-1$, idempotents.4.1, 4.3.
10Cyclic codes (ctd.)Zeroes & minimum distance (BCH-bound)4.4–4.5.
11BCH codes Designed distance, dimension5.1.
12BCH codes (ctd.)Reed–Solomon codes5.2.
13 Cancelled Lectures
14 Easter Break
15 BCH codes (ctd.) Decoding, Berlekamp–Massey. 5.4.2.
16Convolutional codesEncoding, state & trellis diagrams & Viterbi decoding14.1–14.5.
17Recap
22Exam All of the above.