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<p>Creating course page via bot</p> <p><b>New page</b></p><div>{{Infobox Course<br /> | code = MTL744<br /> | name = Mathematical Theory of Coding<br /> | credits = 3<br /> | credit_structure = 3-0-0<br /> | pre_requisites = MTL105/MTL501<br /> | overlaps = ELL710<br /> }}<br /> <br /> == MTL744 : Mathematical Theory of Coding ==<br /> 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: Sphere-covering 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 Reed-Solomon codes, Alternant codes, Goppa codes, Sudan decoding for generalized RS codes.</div>

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