Course detail

Coding in Informatics

FEKT-FKODAcad. year: 2017/2018

Students will get aquainted with basic concepts of the coding theory and broaden their mathematical knowledge of algebra and number theory.

Learning outcomes of the course unit

After completing the course, students should be able to:
- construct the shortest binary code using the Huffman algorithm;
- find the minimum distance of a block code;
- decide about the linearity of a block code;
- deduce the generator and parity-check matrices of a linear code;
- decode with the nearest neighbour method and using syndromes.

Prerequisites

Students should have the knowledge of linear algebra and combinatorics at the bachelor degree level; in particular, they shoud be able to add and multiply vectors matrices, solve systems of linear equations, and compute the number of choices of k elements from an n-element set.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Not applicable.

Planned learning activities and teaching methods

Teaching methods are specified in Article 7 of Study and Examination Regulations.

Assesment methods and criteria linked to learning outcomes

Maximum 25 points for control tests and activities during the semester (at least 10 points for the course-unit credit); maximum 75 points for a written exam.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

1. Basic concepts of coding theory. Huffman construction of shortest code.
2. Block codes. Hamming distance.
3. Error detection and error correction.
4. Main coding theory problem. Perfect codes.
5. Basic algebraic notions - group, field, vector space.
6. Linear codes.
7. Generator and parity-check matrices.
8. Decoding linear codes. Syndromes.
9. Hamming codes.
10. Golay codes.
11. Reed-Muller codes.
12. Cyclic codes.

Aims

The goal of the course is to explain basic concepts and computational methods of the coding theory.

Specification of controlled education, way of implementation and compensation for absences

Lectures are not compulsory, practice classes are compulsory.

Classification of course in study plans

  • Programme BTBIO-F Master's

    branch F-BTB , 1. year of study, summer semester, 5 credits, compulsory

  • Programme EEKR-CZV lifelong learning

    branch ET-CZV , 1. year of study, summer semester, 5 credits, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Computer exercise

26 hours, compulsory

Teacher / Lecturer