# 457-0924/01 – Coding Theory (TKDRS)

 Gurantor department Department of Applied Mathematics Credits 10 Subject guarantor doc. Mgr. Petr Kovář, Ph.D. Subject version guarantor doc. Mgr. Petr Kovář, Ph.D. Study level postgraduate Requirement Choice-compulsory Year Semester winter + summer Study language Czech Year of introduction 2000/2001 Year of cancellation 2009/2010 Intended for the faculties Intended for study types Doctoral
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.

### 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)
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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