Coding Theory

Class overview

This lecture course will provide Master students in Math with some basic concepts of coding theory and applications.

Organization:

+ 3 hours/ week (including exercise sessions)

+ Time of Lecture Course: 8:00-11:30  (Monday, Wednesday, Friday)

+ Exercise Class: 8:00-11:30  (Monday, Wednesday, Friday)

+ Room: Building L, Third Floor, Seminar Room 2 (Faculty of Math)

+ Written final examination (90-120 minutes)

Literature

[1] J. H. van Lint, Introduction to Coding Theory, Third Edition, Springer 1999.

[2] J. Bierbrauer, Introduction to Coding Theory, Chapman and Hall-CRC, 2017.

[3]  R. Roth, Introduction to Coding Theory, Cambridge University Press, 2006.

[4] D. R. Hankerson, Coding Theory and Cryptography: The Essentials, Second Edition, CRC Press, Taylor & Francis Group, 2000.

[5]  I. F. Blake, Essays on Coding Theory, Cambridge University Press, 2024.

[6] S. O. I. Tohăneanu, Commutative Algebra Methods for Coding Theory, De Gruyter, 2024.

[7] O. Moreira (editor), An Introduction to Algebraic and Combinatorial Coding Theory,  Arcler Press, 2024.

[8] Z. Gacovski, Information and Coding Theory in Computer Science, Arcler Press, 2023.

[9] S. T. Dougherty, Algebraic Coding Theory Over Finite Commutative Rings, Springer, 2017. 

[10] S. Ling, C. Xing, Coding theory: a first course, Cambridge University Press, 2004.

Contents of the lecture course

Chapter I: Basic Concepts in Coding Theory 

1.  What is Coding Theory?

2.  Elementary Concepts

3.  Some Basic Algebra 

Chapter II: Linear Codes

4.  Basic Properties of Linear Codes

5.  Construction of Linear Codes

Chapter III: Perfect and Related Codes

6.   Some Bounds for Codes

7.  Perfect Codes and Hamming Codes

8.  Golay Codes

9.  Reed-Muller Codes 

Chapter IV: Cyclic Codes

10.   Introduction to Cyclic Codes 

11. Generator and Parity-Check Matrices 

12. Decoding of Cyclic Codes and Burst-error-correcting codes . 

Chapter V: Some Special Codes

13.   BCH Codes 

14. Reed-Solomon Codes

15. Quadratic-residue Codes 

16. Goppa Codes

 Course Materials

• Lecture 1 and Exercises

• Lecture 2 and Exercises

• Lecture 3 and Exercises

• Lecture 4 and Exercises

• Lecture 5 and Exercises

• Lecture 6 and Exercises

• Lecture 7 and Exercises

• Lecture 8 and Exercises

• Lecture 9 and Exercises

• Lecture 10 and Exercises

Some Further Notes