Gurantor department | Department of Applied Mathematics | Credits | 4 |

Subject guarantor | doc. Mgr. Petr Kovář, Ph.D. | Subject version guarantor | doc. Mgr. Petr Kovář, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | Semester | winter | |

Study language | Czech | ||

Year of introduction | 2016/2017 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

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 | Credit and Examination | 2+2 |

Combined | Credit and Examination | 10+10 |

After passing the course a student will be able:
- use congruences when solving discrete problems,
- describe symmetries of real world problem using groups,
- calculate polynomial operations in modular arithmetics,
- construct selected Galois fields and simple codes based on these,
- construct simple finite vector fields,
- perform comutation on code words in vector notation,
- perform operations on selected codes in matrix notation,
- encode and decode a message in a simple code,
- detect and correct basic mistakes in transmission.

Lectures

Tutorials

The course serves a building block for Coding Theory. The goal is to provide an overview of methods and train relevant skills, that will be used in the Coding Theory course.

R. HILL: A First Course in Coding Theory, Oxford University Press 2006, ISBN 0-19-853803-0.

J. GALLIAN: Contemporary Abstract Algebra, Cegage Learning; 8th edition 2012, ISBN 978-1133599708.

There will be two tests or the students will prepare a project.

There are no further requirements on the student.

Subject has no prerequisities.

Subject has no co-requisities.

1. Congruences, modular arithmetics, binary a q-ary systems.
2. Symmetries and their description, dihedral and cyclic groups.
3. Finite algebraic structures with a single operation, properties and applications,
4. Products, isomorphisms, construction of groups, classification.
5. Finite algebraic structures with two operations, polynomial rings, operations, properties.
6. Fields of prime order, factor rings, examples.
7. Factorization of polynomials, irreducibile polynomials.
8. Construction of Galois fields, properties.
9. Finite vector spaces, construction, examples and applications.
10. Main coding theory problem, sample codes, applications.
11. Codes as vector spaces. Hamming distance. Equivalence of codes.
12. Simple linear and cyclic codes, importance and examples.
13. Encoding and decoding by a linear code, probability of detecting and correcting an error.
14. Further simple codes, codes and Latin squares.

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

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 30 | 10 |

Examination | Examination | 70 | 30 |

Show history

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

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1801T064) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

2019/2020 | (N0612A140004) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1801T064) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1801T064) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1801T064) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan |

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