470-4202/01 – Abstract Algebra in Coding Theory (AvTK)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Mgr. Petr Kovář, Ph.D.Subject version guarantordoc. Mgr. Petr Kovář, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year2Semesterwinter
Study languageCzech
Year of introduction2016/2017Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOV16 doc. Mgr. Petr Kovář, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

After passing the course a student will be able: - use congruences when solving discrete problems, - describe symmetries of real world problem using groups, - calculate polynomial operations in modular arithmetics, - construct selected Galois fields and simple codes based on these, - construct simple finite vector fields, - perform comutation on code words in vector notation, - perform operations on selected codes in matrix notation, - encode and decode a message in a simple code, - detect and correct basic mistakes in transmission.

Teaching methods

Lectures
Tutorials

Summary

The course serves a building block for Coding Theory. The goal is to provide an overview of methods and train relevant skills, that will be used in the Coding Theory course.

Compulsory literature:

R. HILL: A First Course in Coding Theory, Oxford University Press 2006, ISBN 0-19-853803-0.

Recommended literature:

J. GALLIAN: Contemporary Abstract Algebra, Cegage Learning; 8th edition 2012, ISBN 978-1133599708.

Way of continuous check of knowledge in the course of semester

There will be two tests or the students will prepare a project.

E-learning

Další požadavky na studenta

There are no further requirements on the student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Congruences, modular arithmetics, binary a q-ary systems. 2. Symmetries and their description, dihedral and cyclic groups. 3. Finite algebraic structures with a single operation, properties and applications, 4. Products, isomorphisms, construction of groups, classification. 5. Finite algebraic structures with two operations, polynomial rings, operations, properties. 6. Fields of prime order, factor rings, examples. 7. Factorization of polynomials, irreducibile polynomials. 8. Construction of Galois fields, properties. 9. Finite vector spaces, construction, examples and applications. 10. Main coding theory problem, sample codes, applications. 11. Codes as vector spaces. Hamming distance. Equivalence of codes. 12. Simple linear and cyclic codes, importance and examples. 13. Encoding and decoding by a linear code, probability of detecting and correcting an error. 14. Further simple codes, codes and Latin squares.

Conditions for subject completion

Full-time form (validity from: 2016/2017 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  30
Mandatory attendence parzicipation: participation at all exercises is obligatory, 2 apologies are accepted participation at all lectures is expected

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2019/2020 (N2647) Information and Communication Technology (1801T064) Information and Communication Security P Czech Ostrava 2 Optional study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava Optional study plan
2019/2020 (N0612A140004) Information and Communication Security P Czech Ostrava 2 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1801T064) Information and Communication Security P Czech Ostrava 2 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1801T064) Information and Communication Security P Czech Ostrava 2 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1801T064) Information and Communication Security P Czech Ostrava 2 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner