TEW - Linear Algebra, Coding Theory and Cryptography
Speakers and Syllabus
Speakers and Tutors
- Prof. Dinesh Khurana, Professor, Department of Mathematics, Panjab University, Chandigarh.
- Prof. R. B. Bapat, Professor, Indian Statistical Institute (ISI), Delhi.
- Prof. Dhananjoy Dey, Scientist E, DRDO, Delhi.
- Dr. Anuradha Sharma, Associate Professor, Indraprastha Institute of Information Technology (IIIT), Delhi.
Syllabus
- Prof. Dinesh Khurana: Vector spaces, Modules, Finitely generated modules over PIDs and their applications.
- Prof. R. B. Bapat: Nonegative Matrices, Graph associated with a matrix, Brouwer's Fixed Point Theorem, Perron's theorem for positive matrices, strongly connected graphs,irreducibility, Perron-Frobenius theorem for irreducible matrices, primitive, cyclic,reducible matrices (statements and examples), Inequalities for Perron root.
- Prof. Dhananjoy Dey: Finite Fields (including the construction of finite fields),Polynomials over Finite Fields, Applications of Algebra in Cryptography.
- Dr. Anuradha Sharma: Bounds in coding theory: The main coding theory problem, Sphere-covering bound, Gilbert-Varshamov bound, Plotkin bound, Hamming bound and perfect codes, Hamming codes, Golay codes, Singleton bound and MDS codes, Griesmer bound, Construction of linear codes: Propagation rules, Reed-Muller codes, subfield codes, BCH codes: Parameters of BCH codes, Decoding of BCH codes, Reed-Solomon
codes, Quadratic residue codes.
Time Table
Date and Day | 9.30 to 10.30 (Lecture 1) |
10:30 to 11:00 |
11:00 |
12:00 to 1:00 (Leture 3) |
1:00 - 2:00 | 2.00 to 3.00 (Lecture 4) |
3:00 to 3:30 |
3:30 to 4:30 (Discussion) |
4:30 - 5:00 |
18-11-2019 (Monday) | DK | T | DK | RB | L | RB | T | DK | S |
19-11-2019 (Tuesday) | DK | E | DK | RB | U | RB | E | RB | N |
20-11-2019 (Wednesday) | DK | A | DK | DD | N | AS | A | AS | A |
21-11-2019 (Thursday) | RB | AS | AS | C | DD | DD | C | ||
22-11-2019 (Friday) | RB | DD | DD | H | AS | AS | K | ||
23-11-2019 (Saturday) | DD | DD | AS | AS | AS | S |
RB - Prof. R.B. Bapat
DK - Prof. Dinesh Khurana
DD – Prof. Dhananjoy Dey
AS – Dr. Anuradha Sharma