TMA4185 Coding theory - Spring 2016
| Lecturer | Kristian Gjøsteen |
|---|---|
| Schedule | |
| Lectures: | Monday 12.15-14.00 in F3 |
| Thursday 14.15-16.00 in R21 | |
| Visiting hours: | Monday 14.15-15.00 in 848, SBII |
| Exercises: | joint with visiting hours |
Messages
23/6: The results are in. A: 5, B: 5, C: 3, D: 3, E: 3, F: 4.
Some comments:
- 1a: Too many had trouble with this.
- 1c: Too many people gave a parity check matrix for the permutation-equivalent code, not the original code.
- 1d: Syndrome decoding turned out to be hard, and some people forgot they were working over a non-binary field.
- 3: Too many people did not get the difference between upper bounds (no codes better than this exist) and lower bounds (codes at least this good exist).
13/6: This year's exam with suggested solutions.
Book
Huffman and Pless: Fundamentals of Error-Correcting Codes.
You may also find Lindell's lecture notes (available from his course home page) useful.
Exam
The exam will be on June 11, with permitted aids code C. Previous exams are available.
Reference group
| Name | |
|---|---|
| Amirhossein Kazemi | amirhosk at stud.ntnu.no |
| Nicola Bucceroni | nickbucc at hotmail.it |
| Terje Bull Karlsen | terjebul at stud.ntnu.no |
Contents
Chapters from the book:
- 1.1-1.8, 1.10, 1.12.
- 2.1, 2.4, 2.8.
- 3.1-3.7
- 4.1-4.5
- 5.1-5.2, 5.4.1, 5.4.2
- 14.1-14.5
Notes:
Exercise sets
For some of the exercises, you will need to read material from the book that has not been covered in the lectures.
| Week | What |
|---|---|
| 5 | 1.2: 3. 1.3: 4, 6, 7. 1.4: 17, 19. 1.5: 23, 25, 27, 31. 1.6: 34, 35, 37, 39. |
| 7 | 1.7: 45, 46, 48. 1.8: 58. 1.11: 64, 68. 1.12: 82. 2.1: 86, 87, 90, 95. 2.4: 111. 2.8: 131. |
| 8 | 3.1: 152. 3.2: 159. 3.3: 160, 161, 162, 165. 3.4: 169, 170, 173, 174. 3.6: 180. 3.7: 188, 190, 192. |
| 9 | 4.1: 201, 204. 4.2: 207, 209, 213, 214. |
| 14 | 4.3: 220, 221, 223, 224. 4.4: 237, 238, 246, 248. 4.5: 265. 5.2: 291, 299, 300, 301. |
Plan
This plan will change.
| Uke | Hva | Book | Notes |
|---|---|---|---|
| 2 | Shannons teorem | 1.11 | |
| 3 | Linear codes, distance, weight, dual codes. | 1.2, 1.3, 1.4, 1.12 | |
| 4 | Hamming codes, equivalent codes, finite fields | 1.6, 1.8, 3.1, 3.2, 3.6 | |
| 5 | Finite fields, equivalent codes, Reed-Muller codes | 1.10, 3.4, 3.6 | Reed-Muller codes |
| 6 | Bounds on code sizes. Finite fields. | 2.1, 2.4, 2.8, 3.3, 3.7 | |
| 7 | Cyclic codes | 4.2 | |
| 8 | Equivalence of cyclic codes, ideals, polynomial factors and cyclotomic cosets | 4.1-4.4. | |
| 9 | Minimum distance of cyclic codes. Applications. | 4.5, 5.5, 5.6 | |
| 10 | BCH codes. Decoding BCH codes | 5.4 | |
| 11 | BCH codes, Reed-Solomon codes, algebraic geometric codes | 5.1, 5.2 | |
| 12 | Easter holiday | ||
| 13 | Convolution codes | 14.1, 14.3, 14.4, 14.5 | Convolutional codes (Easter holiday on Monday) |
| 14 | Convolution codes | 14.1, 14.3, 14.4, 14.5 | Convolutional codes |
| 15 | Repetition | ||
| 16 | Old exams | ||
| 17 | Old exams | ||