457-0924/01 – 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 introduction2000/2001Year of cancellation2009/2010
Intended for the facultiesIntended for study typesDoctoral
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 2+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
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 Cource in Coding Theory, Clarendon Press, Oxford, 1986.

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

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Úvod. Samoopravné kódy, (n, M, d) - kódy, Hammingova vzdálenost. Hlavní problém teorie kódování. Ekvivalence kódů, nutná a postačující podmínka existence (n, M, d) - kódů, Hammingova hranice, perfektní kódy. Blokove designy v teorii kódování. Blokové designy (BIBDS's), užití (BIBDS's) v kódování. Konečná tělesa a vektorové prostory. Lineární kódy. Výhody a nevýhody lineárních kódů, ekvivalence lineárních kódů, kódování a dekódování lineárními kódy, pravděpodobnost korekce a detekce chyby. Duální kódy. Duální kód, kontrolní matice, syndromové dekódování, nekompletní kódování. Hammingovy kódy. Binární a rozšířené Hammingovy kódy, q-ární Hammingovy kódy, zkracování kódu. Perfektní kódy. Kódy a latinské čtverce. Latinské čtverce a vzájemně ortogonální latinské čtverce, užití latinských čtverců v kódování. Decimální d-e-c-kód a BCH kódy. Vandermondova matice, d-e-c-kód, BCH kódy. Cyklické kódy. Polynomy, cyklické kódy, binární a ternární Golayovy kódy.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

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