SC/IT XXX Modern Topics in Coding Theory and Cryptography
Course Placement: Modern topics in coding theory and cryptography is an elective course for fourth year BTech ICT
program and it is open to MTech and PhD students of ICT program.
Course format: It is 3 hours lecture every week.
Course content: Historical Introduction and Motivation of Coding and Cryptography, Basic Review of Finite Fields
and Finite Rings, Introduction to Algebraic Coding Theory and Mathematical Cryptography, Graph-based codes,
Polar Codes, Compressive Sensing and Codes, Network Coding (single source multiple destinations and multiple
source multiple destinations, cyclic and acyclic networks), Q-Analogs in Coding Theory, Network Coding for
Distributed Storage, Binary and Non-Binary Quantum error correcting codes (Hamming, Hexacodes, Reed Solomon,
BCH codes, quantum cyclic codes), Quantum Codes for Symmetric and Asymmetric Channels, Quantum Codes from
algebraic rings, Quantum Cryptography, Algebraic Geometric Codes, Post-Quantum Cryptography (code-based
cryptography and lattice-based cryptography), Codes, Cryptography and Biology.
Text Book:
1. Raymond Hill, A first course in coding theory, Oxford University Press, 1990 (Elementary Text Book for
Coding Theory)
2. San Ling and Chaoping Xing, Coding Theory: A First Course, Cambridge University Press, 2004.
Reference Book:
1. R.M. Roth, Introduction to Coding Theory, Cambridge University Press, 2006
2. E.R. Berlekamp, Algebraic coding theory, McGraw-Hill, 1968. Revised edition published by Aegean Park
Press in 1984.
3. R.E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2002.
4. W.C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003.
5. S. Lin and D.J. Costello, Error Control Coding (2nd edition), Prentice-Hall, 2004.
6. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North-Holland, 1977.
7. R.J. McEliece, Theory of Information and Coding (2nd edition), Cambridge University Press, 2002.
Research Papers : Many research papers will be provided as part of the course.
Assessment method: 6 – 8 Assignments, two mid-semester examinations and a final examination. It also has
programming project in applications assessed as bonus marks.
Course Outcomes:
The students after completing the course will get a modern overview of Coding theory, cryptography and its
applications. They will get an insight on how codes are used in various applications (both old and new). It exposes
them various construction algorithms for error correcting problems of ICT. Projects in the course provide first hand
research opportunities in niche and hot area to the students
Through this course students can develop ability to
 Apply the knowledge of mathematics, science, engineering fundamentals, and engg.
specialization to the solution of complex engineering problems (P1)
 understand and create mathematical arguments for solving problems (P2)
 understand mathematical structures such as algebra, graphs, trees and learn their uses
(P12)
 develop skills towards mathematical modeling and analysis of engineering problems (P3,
P4)
P1
X
P2
X
P3
X
P4
X
P5
P6
P7
P8
P9
P10
P11
P12
X
Lecture Schedule
1
2
3
4
Sl. No.
Week 1
1.1
Week 2
2.1
Week 3
3.1
3.2
Week 4
4.1
4.2
Description
No. of Lectures
3
Introduction
3
Graph-based codes: Expander Codes
3
Polar Codes
Compressive Sensing and Codes
3
Network Coding - SSMD
Network Coding - MSMD
5
3
Week 5
6
7
8
5.1
Week 6
6.1
6.2
Week 7
7.1
7.2
7.3
7.4
Week 8
Q-Analogs in Coding Theory
3
Network Coding for Distributed Storage
Regenerating Codes and Fractional Repetition Codes
3
Binary and Non-Binary Quantum error correcting codes
Quantum Hamming, Hexacodes, Reed Solomon and Reed Muller Code
Quantum BCH codes, quantum cyclic codes
Quantum Codes for Asymmetric Channels
3
Quantum Cryptography
9
Week 9
10
Week 10
3
Algebraic Geometric Codes
3
Post-Quantum Cryptography - Introduction
11
Week 11
3
Code-based cryptography
12
Week 12
3
Lattice-based cryptography
13
Week 13
3
Codes and Biology
14
Week 14
Cryptography and Biology
3