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.
- Prof. Madhu Raka, Professor, Department of Mathematics, Panjab University, Chandigarh.
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.
- Prof. Madhu Raka: 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
Time Table:
Date and Day |
9.30 (Lecture 1) |
10:30 |
11:00 (Lecture2) |
12:00 (Leture 3) |
1:00 2:00
|
2.00 (Lecture 4) |
3:00 3:30
|
3:30 (Discussion) |
18-11-2019 (Monday) |
DK |
|
DK |
RB |
|
RB |
|
DK |
19-11-2019 (Tuesday) |
DK |
DK |
RB |
RB |
RB |
|||
20-11-2019 (Wednesday) |
DK |
DK |
DK |
DD |
DD |
|||
21-11-2019 (Thursday) |
RB |
DD |
DD |
MR |
MR |
|||
22-11-2019 (Friday) |
DD |
DD |
MR |
MR |
MR |
|||
23-11-2019 (Saturday) |
MR |
MR |
DD |
DD |
DD |
(Tea Breaks: 10.30-11:00, 3.00-3:30; Lunch: 1:00-2:00; Snacks: 4:30 - 5.00)
- RB - Prof. R.B. Bapat
- DK - Prof. Dinesh Khurana
- DD – Prof. Dhananjoy Dey
- MR – Prof. Madhu Raka