# Coding Theory (MATH326) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Coding Theory MATH326 3 0 0 3 6
Pre-requisite Course(s)
Math 332
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer. This course is designed to introduce the basic concepts of Coding Theory. The students who succeeded in this course; Understand and use the basic parameters of a code Understand the structure of finite fields and make computations over finite fields Find generator matrices and parity-check matrices of a linear code Encode and decode with a linear code Encode and decode with cyclic codes Error detection, correction and decoding, finite fields, linear codes, bounds in coding theory, construction of linear codes, cyclic codes.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Error Detection, Correction and Decoding pp. 5-14
2 Fields (review), Polynomial Rings (review), Structure Of Finite Fields pp. 17-26, pp. 26-30
3 Minimal Polynomials, Vector Spaces Over Finite Fields pp. 30-35, pp. 39-44
4 Linear Codes, Hamming Weight, Bases For Linear Codes pp. 45-52
5 Generator Matrix and Parity-check Matrix, Equivalence of Linear Codes, Encoding with a Linear Code, Decoding with a Linear Code pp. 52-59
6 Cosets, Nearest Neighbourhood Decoding For Linear Codes, Syndrome Decoding pp. 59-66
7 Midterm Exam
8 Some Bounds In Coding Theory pp. 75-84
9 Hamming Codes, Golay codes, Singleton bound and MDS codes pp. 84-95
10 Construction Of Linear Codes pp. 113-126
11 Cyclic Codes pp. 133-145
12 Decoding Of Cyclic Codes pp. 145-150
13 BCH codes pp. 159-168
14 Decoding of BCH codes, Reed-Solomon codes pp. 168-175
15 Review
16 Final Exam

### Sources

Course Book 1. Coding Theory, A First Course, San Ling, Chaoping Xing, Cambridge University Press, 2004 2. Introduction to Coding Theory, J. H. Van Lint, Springer, 1999

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 4 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 7 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 3 48
Presentation/Seminar Prepration
Project
Report
Homework Assignments 4 9 36
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 13 26
Prepration of Final Exams/Final Jury