Sep 13: Introduction to the course. History and basics of finite fields.
What is coding theory.
Sep 15: Linear codes: coding and decoding schemes; parity-matrix H;
linear (n,k) code; dimension and length; code words. Examples of codes
(parity-check code and repetition code), detecting and correcting errors.
Sep 20: Repetition codes (cont). Canonical generator matrix.
Channels: binary symmetric channel and Gaussian channel. Capacity of
the channel and Shannon theorem. Probability of error.
Sep 22: Hamming distance, Hamming weight and t-error-correcting codes.
Minimum distance of a code and its relation to t-error-correcting codes.
Alternative characterization as linearly independent columns of the
parity-check matrix H.
Sep 27: Decoding linear codes. Cosets. Coset leader. Syndrome.
Decoding algorithm. Hamming bound.
Sep 29: Hamming bound (cont). Dual codes and properties. Hamming
codes: definition and proof of 1-error-correction.
[A1 handed out.]
To October lectures.