Finite geometries

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Finite geometries

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Code:	92955
ECTS:	5.0
Lecturers in charge:	prof. dr. sc. Juraj Šiftar
English level: 1,0,0	All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

Load:

1. komponenta

Lecture type Total

Lectures 45

* Load is given in academic hour (1 academic hour = 45 minutes)

Description:

COURSE AIMS AND OBJECTIVES:
This course is a brief overview of design theory. Emphasis is put on connections with similar geometric, combinatorial and algebraic structures, and applications in coding theory, cryptography and statistics.

COURSE DESCRIPTION AND SYLLABUS:
1. Designs. Incidence matrices. Isomorphism and automorphism. Necessary existence conditions.
2. Basic construction methods for block designs.
3. Symmetric designs. Difference family constructions.
4. Hadamard matrices and designs.
5. Finite projective and affine planes.
6. Bruck - Ryser - Chowla theorem.
7. Collineation (automorphism) groups.
8. Error correcting codes.
9. Links between designs and linear codes.
10. Steiner triple systems and quasigroups.
11. Latin squares, orthogonality and generalizations.
12. Some applications of designs in cryptography.
13. Some applications of designs in statistics.

Literature:

1. semester Not active

Izborni predmet 1, 2 - Regular study - Computer Science and Mathematics

2. semester

Izborni predmet 1, 2 - Regular study - Computer Science and Mathematics

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Finite geometries

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FACULTY OF SCIENCE