FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 499 | Course Introduction and Application Information
| Course Name |
Introduction to Coding Theory
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 499
|
Fall/Spring
|
3
|
0
|
3
|
6
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
First Cycle
|
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | The aim of this course is to introduce the basic theory and applied topics of error correcting codes. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | This course provides an introduction to error correcting codes by which it is possible to communicate on noisy channels, such as satellite communications. In this course, an introduction revealing the theory and also an introduction providing important classes of codes is aimed. Topics include: linear codes, Hamming codes as perfect codes, nonlinear codes, Hadamard codes, dual codes and weight distributions, cyclic codes, and BCH codes. Requirements for the course are basic linear algebra and an elementary number theory. |
|
|
Core Courses | |
| Major Area Courses |
X
|
|
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Finite fields | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 2 | Linear codes and their parameters, their properties | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 3 | Error probability and Shannon's theorem | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 4 | Hamming codes | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 5 | New codes from old | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 6 | Nonlinear codes, Plotkin bound | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 7 | Hadamard matrices and Hadamard codes | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 8 | Examples of nonlinear codes | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 9 | BCH codes – an example | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 10 | Dual codes | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 11 | Weight distributions and properties | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 12 | Cyclic codes | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 13 | Properties of cyclic codes | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 14 | BCH codes continued | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| 15 | Semester Review | |
| 16 | Final Exam |
| Course Notes/Textbooks | “The Theory of ErrorCorrecting Codes” by F. J. MacWilliams, N. J. A. Sloane, North Holland Publishing Co, Vol.16, 1977. ISBN-13: 978-0444851932 |
| Suggested Readings/Materials | “Introduction to Coding Theory” by J. H. van Lint, GTM, Springer, 3rd Edition, 1999. Online ISBN: 978-3-642-58575-3 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
10
|
20
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
2
|
40
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
12
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
14
|
3
|
42
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
10
|
3
|
30
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
20
|
40
|
| Final Exam |
1
|
20
|
20
|
| Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
|||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
X | ||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
X | ||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
|||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
|||||
| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
|||||
| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
|||||
| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
|||||
| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
|||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
|||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
|||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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