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Kode, njihovi ohranjevalci in pripadajoče incidenčne strukture / Codes, their preservers, and corresponding incidence structures

Naziv

Tittle

Kode, njihovi ohranjevalci in pripadajoče incidenčne strukture / Codes, their preservers, and corresponding incidence structures

Akronim

Acronim

BI-HR/20-21-038

Opis

Description

(SI) Teorija kodiranja predstavlja pomembno raziskovalno področje v matematiki s številnimi vplivi na realno življenje. V zadnjem desetletju se je signifikantnost teorije kodiranja dvignila na ekstremen nivo, saj se potreba za efektivno in varno shranjevanje podatkov s spleta povečuje eksponentno. Z matematičnega vidika teorija kodiranja preučuje objekte iz linearne algebre, pri čemer so koeficienti matrik iz končnega obsega. Drugo raziskovalno področje iz matrične teorije predstavljajo ohranjevalski problemi. Slednji zahtevajo karakterizacijo vseh preslikav med dvema matematičnima strukturama, ki ohranjajo neko dano invarianto. Obe raziskovalni temi so v sorodu s teorijo grafov, še posebej z grafi, ki premorejo dovolj simetrije ali pa imajo lepe kombinatorične lastnosti. V projektu nameravamo kombinirati vsa tri omenjena področja, korist slednjega bodo novi raziskovalni rezultati. V projektu bomo preučevali kode, ki so pridobljene iz incidenčnih relacij na številnih matematičnih objektih.
(EN) Coding theory is an important research area in mathematics with many implications for real life. In the last decade, the significance of coding theory has risen to an extreme level, as the need for efficient and secure storage of data from the web increases exponentially. From a mathematical point of view, coding theory studies objects in linear algebra, where the coefficients of the matrices are from a finite range. Another area of research in matrix theory is conservation problems. The latter requires the characterization of all mappings between two mathematical structures that preserve some given invariant. Both research topics are related to graph theory, in particular to graphs that have sufficient symmetry or have nice combinatorial properties. In this project we intend to combine all three of these areas, the benefit of the latter being new research results. In this project, we will study codes that are obtained from incidence relations on a number of mathematical objects.

Trajanje

Duration

01/01/2020 - 31/12/2022

Vodja projekta

Project Leader

Marko Orel

Sodelujoče organizacije

Participating organizations

University of Rijeka, Department of Mathematics

Oddelek

Department

Oddelek za matematiko IAM
University of Primorska

Andrej Marušič Institute
UP IAM

Muzejski trg 2
6000 Koper
Slovenia

tel.: +386 (0)5 611 75 91
fax.: +386 (0)5 611 75 92
e-mail: info@iam.upr.si
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