| Course Unit Code | 470-4203/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| KOV16 | doc. Mgr. Petr Kovář, Ph.D. |
| Summary |
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| 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. |
| Learning Outcomes of the Course Unit |
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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 |
| Course Contents |
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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.
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| Recommended or Required Reading |
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| Required Reading: |
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| - R. Hill: A First Course in Coding Theory, Oxford University Press, (2009), ISBN 978-0-19-853803-5. |
- R. Hill: A First Course in Coding Theory, Oxford University Press, (2009), ISBN 978-0-19-853803-5.
- Kovářová: teorie kódování, pracovní text, 2006 |
| Recommended Reading: |
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| - D. R. Hankerson et. al. Coding Theory and Cryptography, 2nd edition, CRC Press, (2000), ISBN 0-8247-0465-7 |
| - D. R. Hankerson et. al. Coding Theory and Cryptography, 2nd edition, CRC Press, (2000), ISBN 0-8247-0465-7 |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 20 (20) | 10 |
| Project in Coding Theory | Project | 20 | 10 |
| Examination | Examination | 80 (80) | 41 |
| Written part | Written examination | 60 | 31 |
| Oral part | Oral examination | 20 | 5 |