| Course Objectives: |
The goal of the theory is to construct efficient codes with a high error correcting capability with fast encoding and decoding mathematical algorithms. The main goal of the course is to introduce coding theory and its basics. The course is a graduate level course with the subject from a mathematical, engineering, or computer science background.
|
| Course Content: |
The channel coding, Galois fields, linear codes over finite fields, encoding and decoding with a linear code, self-dual codes, obtaining new codes, cyclic codes, optimal codes, upper and lower bounds for codes, MacWilliams Relations, some important families of codes: Hamming codes, Golay codes, Reed Muller codes, Reed Solomon codes. |
| Week |
Subject |
Related Preparation |
| 1) |
Error correction and the probability theory, basic definitions in classical coding theory, linear codes, generating and parity check matrices, dual codes, weights and distances. |
Course Book |
| 2) |
Obtaining new codes from old, equivalence of codes, Hamming codes, Golay codes, Reed Muller codes. |
Course Book |
| 3) |
Encoding, decoding, Nearest Neighbour decoding, cosets, syndrome decoding. |
Course Book |
| 4) |
Singleton bound and MDS codes, sphere packing bound and perfect codes, Plotkin bound, The linear programming bound, Griesmer bound. |
Course Book |
| 5) |
Introduction to finite fields and basic definitions, polinomials and the Euclidean algorithm, construction of finite fields, subfields. |
Course Book |
| 6) |
Cyclotomic cosets and minimal polinomials, trace and subfield codes., factoring the polynomial x^n-1, basic definitions and theorems for cyclic codes, idempotents, zeros of a cyclic code. |
Course Book |
| 7) |
Cyclic codes and applications on Magma, BCH codes, encoding and decoding with BCH codes. |
Course Book |
| 8) |
Midterm |
|
| 9) |
MacWilliams idenities, the structure and the properties of self-dual codes, construction of self-dual codes. |
Course Book |
| 10) |
Some important self-dual codes (Hamming codes, Golay codes), Reed Solomon codes, generalized Reed–Solomon codes. |
Course Book |
| 11) |
Alternant codes and Goppa codes and their structures. |
Course Book |
| 12) |
Introduction to algebraic geometry, affine space, projective space, algebraic curves, algebraic-geometry codes. |
Course Book |
| 13) |
Introduction to cryptography, basic cryptographic algortihms, Goppa codes and the decoding problem. |
Course Book |
| 14) |
Niderrieter cryptosystem, McEliece cryptosystem |
Course Book |
| 15) |
Shor algoritması, sistem saldırıları. |
Course Book |
| |
Program Outcomes |
Level of Contribution |
| 1) |
Ability to reach wide and deep knowledge through scientific research in the field of Computer Science and Engineering, evaluate, interpret and apply. |
4 |
| 2) |
Ability to use scientific methods to cover and apply limited or missing knowledge, and to integrate the knowledge of different disciplines. |
4 |
| 3) |
Ability to construct Computer Science and Engineering problems, develop methods to solve the problems and use innovative methods in the solution. |
4 |
| 4) |
Ability to develop new and/or original ideas and algorithm; develop innovative solutions in the design of system, component or process. |
4 |
| 5) |
Ability to have extensive knowledge about current techniques and methods applied in Computer Engineering and their constraints. |
3 |
| 6) |
Ability to design and implement analytical modeling and experimental research, solve and interpret complex situations encountered in the process. |
2 |
| 7) |
Ability to use a foreign language (English) at least at the level of
European Language Portfolio B2 in verbal and written communication. |
3 |
| 8) |
Ability to lead in multidisciplinary teams, develop solutions to complex situations and take responsibility. |
4 |
| 9) |
Awareness of the social, legal, ethical and moral values, and the ability to conduct research and implementation work within the framework of these values. |
3 |
| 10) |
Awareness of the new and emerging applications in Computer Science and Engineering field, and the ability to examine them and learn if necessary. |
5 |
BİLGİ PAKETİ / DERS KATALOĞU
