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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4082 CODING THEORY ELECTIVE 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics (English)

Course Objective

The purpose of this course is to provide the students with a firm grounding in the basics of coding theory.

Learning Outcomes of the Course Unit

1   will be able to learn how to construct certain error correcting codes, how to code and decode. 2   will be able to reinforces knowledge of algebra and linear algebra. 3   will be able to see how a problem coming from the application is transformed into a mathematical problem and see how solutions are produced using the tools learned before.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Structure of Finite Fields and Examples 2 Error detection, correction and decoding. Hamming distance. Linear Codes 3 Generator matrix and parity-check matrix. 4 Decoding of linear codes. Syndrome decoding. 5 Bounds in coding theory.The main coding theory problem. Hamming codes. 6 Golay codes. Singleton bound and MDS codes. 7 Reed-Muller codes. Subfield codes. 8 Problems and discussion 9 Cyclic codes. 10 Cyclic codes (continues) 11 Decoding of cyclic codes. 12 BCH codes. 13 Reed Solomon codes. 14 Sudan decoding for generalized RS codes.

Recomended or Required Reading

Textbook(s): San Ling, Chaoping Xing, Coding Theory, a first course, Cambridge University Press 2004 Supplementary Book(s): F. J. MacWilliams, N. J. A. Sloane, The Theory of Error Correcting Codes, North Holland Publishing Co, 1977. References: Materials:

Planned Learning Activities and Teaching Methods

Lecture Notes Problem Solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Vize 2 FN Final 3 BNS BNS VZ * 0.40 + FN * 0.60 4 BUT Bütünleme Notu 5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

Midterm and Final exam

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

To be announced.

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparations before/after weekly lectures 13 5 65 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 5 3 4 3 5 3 3 3 LO.2 4 5 3 3 5 3 3 LO.3 5 5 3 4 3 5 3 3 3