Theory of Codes

Course guarantor:

Edita Pelantová

Lecturer:

Kateřina Horaisová

Tutor:

Kateřina Horaisová

Supervisor:

Department of Software Engineering

Synopsis:

Algebraic methods used in error detecting and error correcting codes.

Requirements:

Basic results and techniques in linear algebra and general algebra, particularly knowledge of finite fields.

Syllabus of lectures:

Error detecting and error correcting codes, minimum distance of a code, the Hamming bound.

Codes with the best parameters, the Hadamard matrices, Levenshtein theorem.

Linear codes: the generator and parity-check matrices, standard decoding, Hamming codes, cyclic codes, BCH codes.

Syllabus of tutorials:

Study Objective:

To acquaint students with using results of linear and general algebra for creating error detecting and error correcting codes and their decoding methods.

Study materials:

Obligatory:

Blahut R.E.: Theory and Practice of Error Control Codes. Addison-Wesley, Massachusetts, 1984.

Optional:

F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland: New York, NY, 1978.

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Applications of Informatics in Natural Sciences (compulsory course in the program)