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| credits = 3
| credits = 3
| credit_structure = 3-0-0
| credit_structure = 3-0-0
| pre_requisites = MTL105/MTL501
| pre_requisites = [[MTL105]]/[[MTL501]]
| overlaps = ELL710
| overlaps = [[ELL710]]
}}
}}


== MTL744 : Mathematical Theory of Coding ==
== MTL744 : Mathematical Theory of Coding ==
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.
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.

Latest revision as of 16:43, 14 April 2026

MTL744
Mathematical Theory of Coding
Credits 3
Structure 3-0-0
Pre-requisites MTL105/MTL501
Overlaps ELL710

MTL744 : Mathematical Theory of Coding

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.