Algebraic Coding Theory

Code: MA505 | L-T-P-C: 3-0-0-6

 Prerequisites: MA521 Modern Algebra

Binary group codes, Hamming codes, Polynomial codes, Block codes, Linear codes,Generator and check matrices, Sphere packing, Gilbert-Varshamov and Griesmer bounds, Syndrome decoding. The structure of cyclic codes, Reed Mueller codes, Simplex codes. Nonlinear codes, Golay, Hadamard, Justeen, Kerdock, Nordstorm-Robinson codes. Weight distribution of codes, Generalized BCH codes (including the BCH bound and decoding methods), Self-dual codes and invariant theory, MacWilliams identities and Gleason's theorems on self-dual codes, Covering radius problem, Convolutional codes. Reed-Solomon codes, Quadratic-residue codes and perfect codes. The group of a code, permutation and monomial groups, Mathieu groups, General linear and affine groups, Connections with design theory, Steiner systems, Projective and affine planes.

Texts:

1. Hill, A First Course in Coding Theory, Oxford University Press, 1989.
2. V. Pless, Introduction to the Theory of Error-Correcting Codes, 3rd edition, John Wiley, 1998.