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 type B |

Year | Semester | winter + summer | |

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Doctoral |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

KOV16 | doc. Mgr. Petr Kovář, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Examination | 28+0 |

Part-time | Examination | 28+0 |

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.

Lectures

Individual consultations

Tutorials

Project work

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.

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

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.

Active participation during lectures. Project - progress consulting. The exam has a written and oral part.

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Examination | Examination |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (P0541D170006) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P0541D170006) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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