TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT404 |
| Name | Algebraic Coding Theory |
| Term | 2021-2022 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. YILMAZ DURĞUN |
| Course Instructor |
Prof. Dr. YILMAZ DURĞUN
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to give the necessary information about the Algebraic Coding Theory and to form the basis for this subject. In addition, the application of coding theory to daily life will be discussed. After taking this course, students are expected to have knowledge about the fundamentals of algebraic coding theory, to understand the algebraic structures used in coding theory and to comprehend the examples of how these algebraic structures are applied to communication systems.
Course Content
Error detection, correction and decoding, Fundamental problem of coding theory, Finite fields and minimal polynomials, Vector spaces on finite fields, linear codes, Hamming weight, Some of the linear codes, generator and control matrix, Dual Code, Equivalence of linear codes, Upper and lower Bounds, Hamming Codes, Construction of Linear Codes, Cyclical Codes, Decoding Cyclical Codes
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Students will learn the principles of coding techniques used in communication systems. |
| LO02 | Students will learn linear codes including coding and decoding techniques in detail. |
| LO03 | Students will learn how to apply linear algebra and field theory. |
| LO04 | Students will learn bounds for codes. |
| LO05 | Students will learn the important codes of algebraic coding theory. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 2 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 4 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 2 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 3 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 5 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 3 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 4 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 3 |
| PLO12 | - | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 4 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 4 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 2 |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 4 |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 5 |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 5 |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 5 |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Professional and ethical responsibility | Related subjects in the course books | |
| 2 | The fundamental problem of coding theory | Related subjects in the course books | |
| 3 | Finite fields and minimal polynomials | Related subjects in the course books | |
| 4 | Vector spaces over finite fields, linear codes, Hamming Weight | Related subjects in the course books | |
| 5 | Bases for linear codes, generator and parity-check matrix for linear codes | Related subjects in the course books | |
| 6 | Dual code and Decoding | Related subjects in the course books | |
| 7 | Equivalence of linear codes, coding and decoding with linear codes | Related subjects in the course books | |
| 8 | Mid-Term Exam | Related subjects in the course books | |
| 9 | Upper and Lower Bounds | Related subjects in the course books | |
| 10 | Hamming Codes | Related subjects in the course books | |
| 11 | Construction of Linear Codes | Related subjects in the course books | |
| 12 | Cyclic Codes | Related subjects in the course books | |
| 13 | Decoding of cyclic codes | Related subjects in the course books | |
| 14 | BCH kodları | Related subjects in the course books | |
| 15 | Reed Solomon codes | Related subjects in the course books | |
| 16 | Term Exams | Related subjects in the course books | |
| 17 | Term Exams | Related subjects in the course books |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 1 | 2 |
| Mid-term Exams (Written, Oral, etc.) | 2 | 2 | 4 |
| Final Exam | 1 | 2 | 2 |
| Total Workload (Hour) | 134 | ||
| Total Workload / 25 (h) | 5,36 | ||
| ECTS | 5 ECTS | ||