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Information
| Code | MT007 |
| Name | Error Correcting Codes I |
| Term | 2022-2023 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. YILMAZ DURĞUN |
| Course Instructor |
1 |
Course Goal / Objective
The goal is that the student shall learn some classical constructions of good error correcting codes and to learn some classical results in coding theory as for example the Macwilliams identities for linear and nonlinear error correcting codes.
Course Content
Basics in error correcting. Properties of linear codes. Shannon's theorem on the existence of good codes. Weight distribution of the dual of a binary linear code, group characters and codes, the theorems of Macwilliams, Krawtchouk polynomials. Perfect codes.
Course Precondition
NONE
Resources
Hill, Raymond. A first course in coding theory. Oxford University Press, 1986.
Notes
Fundamentals of Error-Correcting Codes, 2003 W. Cary Huffman, Vera Pless
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Basics in error correcting. Properties of linear codes. |
| LO02 | Shannon's theorem on the existence of good codes. |
| LO03 | Weight distribution of the dual of a binary linear code, group characters and codes, |
| LO04 | the theorems of Macwilliams, Krawtchouk polynomials. |
| LO05 | Perfect codes, Goppa Codes |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 2 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Communication channels, Maximum likelihood decoding, Hamming distance | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Nearest neighbour/minimum distance decoding, Distance of a code | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Finite fields, minimal polynomials | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Linear codes, Lower bounds | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Hamming bound and perfect codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Plotkin bound, Nonlinear codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Griesmer bound | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Linear programming bound | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Constructions of linear codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Cyclic codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Cyclic GRS codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | Reed-Solomon codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Hamming codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | BCH codes | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||