Course detail

Coding in Informatics

FEKT-MPC-KODAcad. year: 2024/2025

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)

Entry knowledge

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.

Rules for evaluation and completion of the course

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.

Aims

The goal of the course is to explain basic concepts and computational methods of the coding theory, namely
- construction of the shortest binary code using the Huffman algorithm;
- finding the minimum distance of a block code;
- deciding about the linearity of a block code;
- deducing the generator and parity-check matrices of a linear code;
- decoding with the nearest neighbour method and using syndromes.

Study aids

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.

Syllabus

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.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Petr Fuchs, Ph.D.