Coding in Informatics
FEKT-MPC-KODAcad. year: 2020/2021
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.
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.
Recommended optional programme components
Recommended or required reading
ADÁMEK, Jiří: Kódování. Praha, SNTL, 1989. (CS)
ZNÁM, Štefan: Teória čísel. Bratislava, Alfa, 1977. (SK)
ROMAN, Steven: Introduction to Coding and Information Theory. Springer-Verlag, 1997. (EN)
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
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.
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 MPC-BTB Master's, 1. year of study, summer semester, 5 credits, compulsory-optional