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Code: | M4081 | Acronym: | M4081 |

Keywords | |
---|---|

Classification | Keyword |

OFICIAL | Mathematics |

Active? | Yes |

Responsible unit: | Department of Mathematics |

Course/CS Responsible: | Master's degree in Mathematical Engineering |

Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|

M:ENM | 6 | Official Study Plan since 2013-2014 | 1 | - | 6 | 56 | 162 |

Teacher | Responsibility |
---|---|

Christian Edgar Lomp |

Theoretical and practical : | 4,00 |

Type | Teacher | Classes | Hour |
---|---|---|---|

Theoretical and practical | Totals | 1 | 4,00 |

Christian Edgar Lomp | 4,00 |

Last updated on 2017-09-19.

Fields changed: Components of Evaluation and Contact Hours, Fórmula de cálculo da classificação final

Fields changed: Components of Evaluation and Contact Hours, Fórmula de cálculo da classificação final

Upon successful completion of this course, the student will:

- Know most of the classical examples of error correcting codes;
- Reproduce key results of the theory and give rigorous and detailed proofs of them.
- Construct new codes from old ones and examine their basic properties.
- Apply the basic techniques, results and concepts of the course to concrete examples and exercises.

Upon successful completion of this course, the student will:

- Know most of the classical examples of error correcting codes;
- Reproduce key results of the theory and give rigorous and detailed proofs of them.
- Construct new codes from old ones and examine their basic properties.
- Apply the basic techniques, results and concepts of the course to concrete examples and exercises.

Linear Algebra over fields.

Theory of Finite Fields.

The course will provide an introduction into the theory of error correcting codes. The following syllabus is a more algebraic approach to this course:

- Shannon’s Theory: Models of communication, probabilistic assumptions and Shannon’s Theorem
- Block codes on arbitrary sets and Hamming metric
- Isometries of codes and basic constructions
- Bounds on codes (Singelton, Gilbert-Varshamov and Haming bound) with their classical codes: MDS, perfect and Hamming codes
- Block codes over groups (parity check codes)
- Block codes over fields (Revision of linear algebra over finite fields)
- Dual code and the MacWilliams’s Theorems
- Examples of codes and their decoding: Golay code and Reed-Solomon code
- BCH-code (Revision of field theory)

Hoffman D. G. 070; Coding theory. ISBN: 0-8247-8611-4

Lint Jacobus H. van; Coding theory. ISBN: 3-540-06363-3

Ling San; Coding theory. ISBN: 0-521-82191-6

Pretzel Oliver; Error-correcting codes and finite fields. ISBN: 0-19-859678-2

MacWilliams F. J.; The theory of error-correcting codes. ISBN: 0-444-85193-3

The content of the lectures is not covered in a single book, but based on some lecture notes by W.Heise and T.Honold (2002, Sofia) as well as and on some lecture notes by V.Aurich (1993, Düsseldorf).

The lectured material is the sole subject of the course and the books indicated in the blbiography are considered to be auxiliar resources for the student.

- Lectures of 4 hours/week

Physical sciences > Mathematics > Algebra > Field theory

Technological sciences > Technology > Information technology

designation | Weight (%) |
---|---|

Exame | 100,00 |

Participação presencial | 0,00 |

Total: |
100,00 |

CF=max( (T1+T2)/2, E)

where Ti is the grade of the ith teste and E is the grade of the grade of the (make-up) exam.

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Page created on: 2019-02-17 at 12:14:31

Page created on: 2019-02-17 at 12:14:31