Diary

Short notes on what has happened and will happen.

12/1: Problem: given unreliable communication channels, how to achieve efficient and reliable communication.

Channels and transmission errors. Detecting or correcting errors? Hamming metric. Codes, coding and decoding. Capacity and Shannon's theorem. Linear codes. Vector spaces over finite fields.

14/1: Finite fields. Vector spaces over finite fields, subspaces and linear maps. Coding and decoding of linear codes. Syndrome decoding.

19/1: Coding and decoding of linear codes. Syndrome decoding. Hamming codes and other simple linear codes.

21/1: Hamming codes.

26/1: Dual codes. Extension, puncture, shortening and combination of codes.

28/1: Reed-Muller codes.

2/2: Reed-Muller codes.

4/2: Bounds on code sizes.

9/2: Bounds on code sizes.

11/2: Factor rings. Finite fields.

16/2: Finite fields. Polynomials.

18/2: Polynomials.

23/2: Field isomorphisms. Minimal polynomials.

25/2: Cyclic codes.

2/3: Cyclic codes. The ring R_n = F[x]/(x^n-1).

4/3: Encoding and parity checking. The structure of R_n and its ideals.

9/3: The structure of R_n and its ideals. Idempotents.

11/3: Duals of cyclic codes. Syndrome decoding of cyclic codes.

16/3: Minimum distance of cyclic codes. BCH codes.

18/3: Linear recurrences. Berlekamp-Massey.

23/3: Berlekamp-Massey. Syndromes, error locator polynomials and decoding.

25/3: Summary of block codes. Power series. Convolutional codes.

8/4: Convolutional codes.

13/4: Convolutional codes.

15/4: Convolutional codes.

20/4: Repetition and exams.

22/4: Repetition and exams. Final lecture.

29/5: Exam.