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 |

Part-time | 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.

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

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

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

Credit | Credit | 30 | 10 | |

Examination | Examination | 70 | 30 | 3 |

Show history

Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

Show history

Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2024/2025 | (N0612A140004) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

2023/2024 | (N0612A140004) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

2022/2023 | (N0612A140004) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2021/2022 | (N0612A140004) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N0612A140004) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (1801T064) Information and Communication Security | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

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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2019/2020 Winter |