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Course, academic year 2023/2024
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Finite Fields - NMMB208
Title: Konečná tělesa
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Is provided by: NMMB337
Guarantor: doc. Mgr. et Mgr. Jan Žemlička, Ph.D.
Class: M Bc. MMIB
Classification: Mathematics > Algebra
Incompatibility : NALG090, NMAG303
Interchangeability : NALG090, NMAG303
Is incompatible with: NMAG303
Is interchangeable with: NMAG303
Annotation -
Last update: G_M (01.06.2015)
The aim of this course is to introduce students to the theory of finite fields. Finite fields are presented both as a useful tool in apllications and and as a model case of an algebraic structure deducible from intuitive operations, but demanding a more abstract approach for effective work. A required course for Information Security.
Course completion requirements - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)

Předmět je zakončen ústní zkouškou.

Literature - Czech
Last update: G_M (01.06.2015)

Lidl, Niederreiter: Finite fields, Cambridge Univ. Press 1997.

Requirements to the exam - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)

Zkouška má ústní formu. Její požadavky odpovídají obsahu přednesené látky.

Syllabus -
Last update: G_M (01.06.2015)

Modular arithmetics for polynomials. Examples of finite fields. Multiplicative group of a finite field. Möbius function. Irreducible, cyclotomic and primitive polynomials. Factorization of polynomials. Basic relationships between block codes and finite fields (generating and control matrices, examples of codes). Quadratic residues. Perron Theorem. Cyclotomic extensions.

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