MT007 Error Correcting Codes I

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT007
Name Error Correcting Codes I
Term 2024-2025 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 Yüksek Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. YILMAZ DURĞUN


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

Update Time: 09.05.2024 11:37