Code Theory B

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

The coding and decoding techniques are described as applications of finite groups, Galoise fields, metric spaces and linear algebra. Modular arithmetic and algebraic extension of finite field are basic tools for code construction. The basic theorems and algorithms are discussed.

Requirements:

Basic knowledges from linear algebra.

Syllabus of lectures:

1.Alphabet, word, code, coding.

2.Finite groups, rings and fields.

3.Encoding and decoding in modular arithmetic.

4.Hamming distance of words and code, error detection, error correction.

5.Elementary methods of coding and decoding.

6.Vector space and linear code.

7.Generating matrix, control matrix, their relationship.

8.Error words, symptoms, decoding via symptom.

9.Binary code, Hamming code.

10.Ring of polynomials, cyclic codes.

11.Galoise fields, generating polynomial, primitive roots.

Syllabus of tutorials:

Study Objective:

Knowledge:

Elements of coding, elements of algebra, linear codes.

Abilities:

Work with rings and fields, finding of generating and control matrix of linear code, finding of generating and control polynom of cyclic code.

Study materials:

Compulsory literature:

[1] J. Adámek: Kódování, SNTL, Praha, 1989.

Recommended literature:

[2] L. Bican, T. Kepka, P. Němec: Úvod do teorie konečných těles a lineárních kódů, SPN, Praha, 1982.

[3] W.W. Peterson: Error-correcting Codes, MIT Press, Cambridge, 1961.

Literatura EN:

1. J. Adámek: Kódování, SNTL, Praha, 1989.

2. L. Bican, T. Kepka, P. Němec: Úvod do teorie konečných těles a lineárních kódů, SPN, Praha, 1982.

3. W.W. Peterson: Error-correcting Codes, MIT Press, Cambridge, 1961.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: