2005 course plan. Notes are available only where there is a pdf link.
Lecture 1   Model of a communication system. Review of mathematical concepts used in coding theory
Lecture 2    Linear codes: examples, definition. Generator and parity-check matrices. Hamming weight. Algorithmic complexity.          
Lecture 3 
  Algorithmic problems of coding theory. Linear codes: correctable errors, standard array.        
Lecture 4 
  Syndrome decoding. Information sets. Information set decoding.      
Lecture 5
   Random binary matrices.The Hamming code, perfect codes. The simplex code.           
Lecture 6    Weight distribution of the Hamming code. Code optimality. Golay codes. Operations on codes.
Lecture 7    Weight distributions. The MacWilliams theorem.Nonlinear codes.
Lecture 8
   Weight distribution for nonbinary codes. Geometric view of codes. Supplementary materisl
                      A linear-algebraic view of the MacWilliams theorem. Nonlinear codes. Delsarte inequalities.

Lecture 9
   Introduction to finite fields.  notes: [pdf]  
Lecture 10  Structure of finite fields.[pdf]                  
Lecture 11  Minimal polynomials, subfields. Uniqueness of Fpm. [pdf]                   
Lecture 12  Cyclotomic cosets and minimal polynomials. [pdf]                   
Lecture 13  Cyclic codes.[pdf]                    
Lecture 14  BCH bound. Nonbinary Hamming codes.[pdf] 
Lecture 15
 Generalizations of the BCH bound: Hartmann-Tzeng, Roos. Fourier transform in finite fields.[pdf]
Lecture 16  Linear complexity. Reed Solomon codes and MDS codes.[pdf]
Lecture 17  Extended RS codes. The Peterson-Gorenstein-Zierler algorithm for BCH decoding. [pdf]
Lecture 18  Forney's algorithm. Evaluation codes. The Berlekamp-Welch decoding algorithm. [pdf] 
Lecture 19  List decoding of codes. Sudan's algorithm for list decoding of RS codes. [pdf]
Lecture 20  The Guruswami-Sudan algorithm, its asymptotic analysis and applications.[pdf]
Lecture  21   Error probability for bounded distance decoding of linear codes. [pdf]
Lecture  22   Error probability of decoding for Reed-Solomon codes. Error probability for maximum likelihood (ML) decoding of binary codes, the union bound. [pdf]
Lecture  23 
Asymptotics of binomial coefficients. The ensemble of random linear codes and the Gilbert-Varshamov bound.
Lecture  24 
Linear codes reach the capacity of the binary symmetric channel
Lecture  25 
The ensemble of random linear codes. Average and typical properties. Reed-Muller codes: definition. [pdf]
Lecture  26 
General properties of RM codes. RM codes of the first order. [pdf]
Lecture  27 
Maximum likelihood decoding of RM(1,m) codes.