470-4203/01 – Coding Theory (TK)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | doc. Mgr. Petr Kovář, Ph.D. | Subject version guarantor | doc. Mgr. Petr Kovář, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2022/2023 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The student should
- analyze the real life problem
- state it as a Coding Theory problem
- solve the problem using means and methods of Coding Theory
- give an interpretation of the solution in the context of the original problem
Teaching methods
Lectures
Tutorials
Project work
Summary
The course gives an overview of basic methods for constructing error-correcting codes suitable for transferring information, as well as the application of Discrete Mathematics and Abstract Algebra in Coding Theory.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Active participation during lectures. Project - progress consulting. The exam has a written and oral part.
E-learning
Other requirements
There are no further requirements defined for the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lecture topics:
1) Introduction. (n, M, d)-codes, Hamming distance
2) Main problem of Coding Theory. Equivalence of codes. Necessary and sufficient condition for the existence of a (n, M, d)-codes, perfect codes.
3) Block designs in Coding Theory.
4) Finite fields and vector spaces.
5) Linear codes. Linear codes, equivalence of linear codes. Coding and decoding, error detection.
6) Dual codes. Syndrome decoding.
7) Hamming codes. Binary and extended Hamming codes.
8) Perfect codes.
9) Cyclic codes. Polynomials, binary a ternary Golay codes.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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