| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Codding Theory | MAT533 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Associate Prof. Dr. Selda ÇALKAVUR
Learning Outcomes of the Course Unit
1) Get all necessary information about the linear codes.
2) Get all necessary information about the Golay codes, Hamming codes, Reed-Muller codes and BCH codes.
3) Get all necessary information about the bounds between the parameters of codes.
4) Get all necessary information about the cyclic codes.
5) Get all necessary information about the codes over Z4.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Linear Algebra
Course Contents
Linear codes, Golay codes, Hamming codes, Reed-Muller codes, BCH codes, cyclic codes, the bounds on the codes, the codes over Z4.
Weekly Schedule
1) Introduction to error-correcting codes, the main coding theory problem2) An introduction to finite fields, Vector spaces over finite fields
3) Introduction to linear codes, Hamming Weight, Equivalence of Linear Codes, Generator Matrix
4) Encoding and Decoding with a Linear Code
5) The Dual Code, The Parity-Check Matrix and Syndrome Decoding
6) Hamming Codes
7) Hamming Codes
8) Perfect Codes
9) Midterm Exam
10) Golay Codes
11) Golay Codes
12) Cyclic Codes
13) BCH Codes
14) Reed-Muller Codes
15) The Codes over Z_{4}
16) Final Exam
Recommended or Required Reading
1- R. Hill, "A Frist Course in Coding Theory", Oxford University.
2- M. Shi, A. Alahmadi, P. Solé, "Codes and Rings", Academic Press, An inprint of Elsevier
3- R. Lidl, H. Niederreiter, "Finite Fields", Encylopedia of Mathematics and its Applications, Cambridge.
Planned Learning Activities and Teaching Methods
1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Simulation
6) Problem Solving
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
30% |
|---|---|
Contribution of Final Examination to Course Grade |
70% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required