Coding Theory
(Lý thuyết Mã hóa)
(Lý thuyết Mã hóa)
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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
What is Coding Theory?
Elementary Concepts
Some Basic Algebra
Chapter II: Linear Codes
Basic Properties of Linear Codes
Construction of Linear Codes
Chapter III: Perfect and Related Codes
Some Bounds for Codes
Perfect Codes and Hamming Codes
Golay Codes
Reed-Muller Codes
Chapter IV: Cyclic Codes
Introduction to Cyclic Codes
Generator and Parity-Check Matrices
Decoding of Cyclic Codes and Burst-error-correcting codes .
Chapter V: Some Special Codes
BCH Codes
Reed-Solomon Codes
Quadratic-residue Codes
Goppa Codes
Course Materials
Lecture 6 and Exercises
Lecture 7 and Exercises
Lecture 8 and Exercises
Lecture 9 and Exercises
Lecture 10 and Exercises
Some Further Notes