TEW - Linear Algebra, Coding Theory and Cryptography

Speakers and Syllabus


Speakers and Tutors

  1. Prof. Dinesh Khurana, Professor, Department of Mathematics, Panjab University, Chandigarh.
  2. Prof. R. B. Bapat, Professor, Indian Statistical Institute (ISI), Delhi.
  3. Prof. Dhananjoy Dey, Scientist E, DRDO, Delhi.
  4. Dr. Anuradha Sharma, Associate Professor, Indraprastha Institute of Information Technology (IIIT), Delhi.

Syllabus

  1. Prof. Dinesh Khurana: Vector spaces, Modules, Finitely generated modules over PIDs and their applications.
  2. 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.
  3. Prof. Dhananjoy Dey: Finite Fields (including the construction of finite fields),Polynomials over Finite Fields, Applications of Algebra in Cryptography.
  4. 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
to
12:00
(Lecture2)

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

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