Syllabus
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Course Code: Elective 3 MMATH21 -312 Course Name: Algebraic Coding Theory |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
|---|---|---|
| 1 | Group codes, elementary properties, matrix encoding techniques. Generator and parity check matrices, polynomial codes. Vector space and polynomial ring, binary representation of numbers, Hamming codes. | |
| 2 | Basic properties of finite fields, irreducible polynomial over finite field, roots of unity. (7.1 to 7.3
of recommended book at Sr. No. 2) Some examples of primitive polynomials, BCH codes. (Chapter 4 of recommended book at Sr. No. 1) |
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| 3 | Linear codes, generator and parity check matrices, dual code of a linear code, Weight distribution of the dual code of a binary linear code, new codes obtained from given codes, cyclic codes, check polynomials, BCH and Hamming codes as cyclic codes, Non-binary Hamming codes, Idempotent , solved examples and invariance property, cyclic codes and group algebras, self dual binary cyclic codes. | |
| 4 | Necessary and sufficient condition for MDS codes, the weight distribution of MDS codes, an existence problem, Read Solomon codes. Hadamard matrices and Hadamard codes.(Chapter 9 and 11 of recommended book at Sr. No. 1) | |
