470-6303/01 – Coding Theory (TKDRS)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantordoc. Mgr. Petr Kovář, Ph.D.Subject version guarantordoc. Mgr. Petr Kovář, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesDoctoral
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 Examination 28+0
Combined Examination 28+0

Subject aims expressed by acquired skills and competences

Each student is supposed to - analyze real life problems - express them as a coding theory problem - solve the problem using coding theory methods - give an interpretation of the theoretical results in the terms of the original problems At the same time he should decide what are the limits of an ideal theoretical solution in contrast to the real situation.

Teaching methods

Lectures
Individual consultations
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 combinatorial approcahes in Coding theory.

Compulsory literature:

Hill: A First Course in Coding Theory, Clarendon Press, Oxford, reprinted 2009.

Recommended literature:

Assmus, Key: Designs and their Codes, University of Cambridge, 1993, ISBN 0-521-458639-0. Hankerson et al.: Coding Theory and Cryptography, 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

Další požadavky na studenta

There are not defined other requirements for 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: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (P0541D170005) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory type B study plan
2019/2020 (P0541D170005) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory type B study plan
2019/2020 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2019/2020 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2018/2019 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2018/2019 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

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