Introduction to linear error correcting codes with an emphasis on the algebraic tools required, including matrices, vector spaces, groups, polynomial rings, and finite fields.
- Fundamentals of Error Correcting, Codes Block codes, Hamming distance, error correction.
- Linear Codes Generator and parity-check matrices, dual codes, Hamming and other perfect codes, standard array decoding.
- Special Linear Codes, Reed Muller codes, self-dual codes, binary Golay codes.
- Finite fields Irreducible polynomials, minimum polynomials, properties of finite fields.
- Cyclic Codes Rings and ideals, cyclic subspaces, generating polynomials, syndrome decoding, burst error decoding.
- BCH Codes - BCH codes and BCH bounds, the Euclidean algorithm and decoding BCH codes.
- Error Correction, Techniques Reed Solomon codes, channel erasures, BCH codes with erasures, interleaving.