Code Theory B

Lecturer:

Tutor:

Supervisor:

Synopsis:

The encryption, decryption, 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.Caesar, Vigenere, affine and Hill method.

5.Public key methods, RSA theory and practice.

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

7.Elementary methods of coding and decoding.

8.Vector space and linear code.

9.Generating matrix, control matrix, their relationship.

10.Error words, symptoms, decoding via symptom.

11.Binary code, Hamming code.

12.Ring of polynomials, cyclic codes.

13.Galoise fields, generating polynomial, primitive roots.

Syllabus of tutorials:

Study Objective:

Knowledge:

Elements of coding and encryption, elements of algebra, linear codes, elementary ciphers, RSA.

Abilities:

Work with rings and fields, finding of generating and control matrix of linear code, encryption by elementary ciphers and RSA.

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:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: