Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
5MATH311CODING THEORY3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The course acquaints student with the mathematics of error correcting codes used in communication and data storage, and their connections with algebra and discrete mathematics.
Course Content information theory, finite fields, linear codes, cyclic codes
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers BERKANT USTAOĞLU
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
Error control coding: fundamentals and applications, by Shu Lin and Daniel J. Costello

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 0 % 0
Quizzes 0 % 0
Homeworks 5 % 8
Other activities 0 % 0
Laboratory works 5 % 8
Projects 0 % 0
Final examination 1 % 20
Total
11
% 36

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 42 3 126
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 5 8 40
Exams and Exam Preparations 5 5 25
Total Work Load   Number of ECTS Credits 6 191

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Recognize and understand mathematical concepts behind error correcting codes.
2 To model and solve practical problems with the assistance of mathematical tools.
3 To master mathematics proof techniques.
4 To identify some special class of problems in computer science and discrete mathematics.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction and application of error correcting codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
2 Fundamental concepts S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
3 Irreducible polynomials S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
4 Finite fields and minimal polynomials S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
5 Introduction to linear codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
6 Generator matrix and dual codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
7 Hamming codes and perfect codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
8 Standard array decoding S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
9 Reed-Muller, self-dual and binary Golay codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
10 Introduction to cyclic codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
11 Rings, ideals and cyclic subspaces S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
12 Generator matrices and parity check matrices for cyclic codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
13 BCH codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
14 Reed-Solomon codes S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
15 Final 1st week S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004
16 Final 2nd week S.A. Vanstone and P. C. van Oorschot “An Introduction to Error Correcting Codes with Applications”, Springer 2004


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 2 2 4 3 2 1 1 1 3 4 4 4 2
C2 4 2 1 4 4 4 4
C3 4 4 4 4 1 2 4 1 4 4
C4 3 4 4 1 4 4 2 2 4 4 3 2

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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