MTL744: Mathematical Theory of Coding

3 Credits (3-0-0)

Pre-requisites: MTL105/MTL501

Overlaps with: ELL710

Review of communication channels, maximum likelihood and nearest neighbour decoding schemes, Hamming distance, Distance of a code. Structure of finite fields,Linear codes and their duals, Equivalence of linear codes, encoding with a linear code, decoding of a linear code, ISBN Code, Hamming codes. Hadamard matrix codes, Golay codes, Codes and Latin squares. Non-linear codes, Nordstrom-Robinson code, Kerdock codes, Preparata codes. Bounds in coding theory: Spherecovering bound, Hamming bound and perfect codes, Singleton bound and MDS codes, Gilbert-Varshamov bound, Plotkin bound, Griesmer bound. Weight enumerators, MacWilliams Identity. Construction of new codes: Propagation rules, Reed-Muller codes, subfield codes.

The structure of cyclic codes, encoding and decoding with a cyclic code, minimal codes, Some special cyclic codes including BCH codes and their decoding algorithm, Reed-Solomon codes, quadratic residue codes. Burst errors, Burst error-correcting codes, decoding of cyclic burst-error-correcting codes. Generalized ReedSolomon codes, Alternant codes, Goppa codes, Sudan decoding for generalized RS codes.