470-4203/02 – Coding Theory (TK)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Mgr. Petr Kovář, Ph.D.Subject version guarantordoc. Mgr. Petr Kovář, Ph.D.
Study levelundergraduate or graduateRequirementOptional
YearSemestersummer
Study languageEnglish
Year of introduction2022/2023Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOV16 doc. Mgr. Petr Kovář, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+10

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:

- R. Hill: A First Course in Coding Theory, Oxford University Press, (2009), ISBN 978-0-19-853803-5.

Recommended literature:

- D. R. Hankerson et. al. Coding Theory and Cryptography, 2nd edition, CRC Press, (2000), ISBN 0-8247-0465-7

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:

Lectures: 1) Error correcting codes, Hamming distance. 2) Main coding theory problem. Necessary and sufficient condition for the existence of a (n, M, d)-code, perfect codes. 3) Block designs (BIBDS's). 4) Finite fields and vector spaces. 5) Linear codes. Coding and decoding, error detection. 6) Dual codes. Syndrome decoding. 7) Hamming codes. Binary and extended Hamming codes. 8) Perfect codes. 9) Latin squares, orthogonal Latin squares. 10) d-e-c-codes a BCH coes. Vandermond matrix. 11) Cyclic codes. Polynomials, binary a ternary Golay codes. During the semester each student prepares one or two projects.

Conditions for subject completion

Full-time form (validity from: 2022/2023 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
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 3
                Written part Written test 60  31
                Oral part Oral examination 20  5
Mandatory attendence participation: Exercises are compulsory and students are expected to participate on the lectures as well.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC P English Ostrava Optional study plan
2024/2025 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava Optional study plan
2023/2024 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC P English Ostrava Optional study plan
2023/2024 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava Optional study plan
2022/2023 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava Optional study plan
2022/2023 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC P English Ostrava Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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