TÜRKÇE
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Information
| Code | MT005 |
| Name | Special Topics in Coding theory |
| Term | 2022-2023 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. YILMAZ DURĞUN |
Course Goal / Objective
This course is an introduction to algebraic coding theory over finite rings and is intended to provide the students with a basic understanding of methods for the construction, evaluation, and application of algebraic coding theory over finite rings.
Course Content
This course is an introduction to algebraic coding theory over finite rings.
Course Precondition
none
Resources
Hill, Raymond. A first course in coding theory. Oxford University Press, 1986.
Notes
Fundamentals of Error-Correcting Codes,2003, Vera Pless and W. Cary Huffman
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learn new information about algebraic coding theory. |
| LO02 | Learns finite rings. |
| LO03 | Learns the module structures on finite rings. |
| LO04 | Learns the structure of linear codes on finite rings. |
| LO05 | Learns dual linear codes and cyclic codes on finite rings. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows the results of previous research in a special field of mathematics | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 3 |
| 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 | 2 |
| 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. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | 5 |
| 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. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have foreign language knowledge 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 | It 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 | Finite fields and finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Principal ideal rings, chain rings an Galois rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Module structure over finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Linear algebra over finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Linear codes over finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Macwilliams identities and extension theorem over finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Linear cyclic codes over finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Free Linear Cyclic codes over finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Quasi-cyclic codes over finite rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Linear codes over finite chain rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Cyclic Codes Over Finite Chain Rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | Some special cyclic Codes Over Finite Chain Rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Linear codes over Galois rings | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | Some cyclic Codes Over Galois Rings | 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 | ||