Course detail

Coding in Informatics

FEKT-MPC-KODAcad. year: 2022/2023

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

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

RNDr. Petr Fuchs, Ph.D.

Department

Department of Mathematics (UMAT)

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.

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.

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.

Work placements

Not applicable.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ADÁMEK, Jiří: Kódování. Praha, SNTL, 1989. (CS)

Recommended reading

ZNÁM, Štefan: Teória čísel. Bratislava, Alfa, 1977. (SK)

Classification of course in study plans

  • Programme MPC-BTB Master's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.