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master's thesis
Teorija kodiranja i linearni kodovi
2017. urn:nbn:hr:126:022370
Lukanović, Marina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

Cite this document

Lukanović, M. (2017). Teorija kodiranja i linearni kodovi (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:022370

Lukanović, Marina. "Teorija kodiranja i linearni kodovi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:022370

Lukanović, Marina. "Teorija kodiranja i linearni kodovi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:022370

Lukanović, M. (2017). 'Teorija kodiranja i linearni kodovi', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 20 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:022370

Lukanović M. Teorija kodiranja i linearni kodovi [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2025 January 20] Available at: https://urn.nsk.hr/urn:nbn:hr:126:022370

M. Lukanović, "Teorija kodiranja i linearni kodovi", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:022370

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Metadata
TitleTeorija kodiranja i linearni kodovi
Title (english)Coding Theory and Linear Codes
AuthorMarina Lukanović
MentorIvan Matić (mentor)
Committee memberDarija Marković (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberLjerka Jukić Matić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2017-07-07, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Današnji je svijet više nego ikad prije svijet informacija te će potreba za što učinkovitijim i pouzdanijim prenošenjem tih informacija samo rasti. Posebno važnu ulogu u tome odigrati će teorija kodiranja. U ovom radu dan je kratak uvod u ovu disciplinu. Da bi se uvidjela njezina važnost, mora se poznavati na koji način funkcioniraju uređaji koji prenose poruke na daljinu te do kakvih pogrešaka može doći prilikom prijenosa informacija. Zbog toga je u prvom poglavlju ukratko objašnjena ova problematika te je opisan opći komunikacijski sustav. Kako bi prijenos informacija bio što učinkovitiji potrebno je uskladiti količinu simbola koji u kodu služe za prijenos informacije sa onima koji služe kao redundacija i omogućavaju ispravljanje pogrešaka. Zato je potrebno konstruirati dobre kodove za koje znamo da postoje zahvaljujući Shannonovom teoremu. Kako bi definirali dovoljno učinkovite kodove potrebno je dodati više strukture prostoru koda. U radu naglasak je stavljen na linearne kodove koje možemo opisati pomoću generirajuće matrice i matrice provjere parnosti. Budući da su u računalima svi podaci prikazani u binarnom brojevnom sustavu, ne iznenaduje činjenica da se i u teoriji kodiranja posebna pozornos posvećuje binarnim kodovima, od kojih je jedan od najpoznatijih koji se dosta često zbog svojih svojstava korsti upravo u memoriji računala binarni Hammingov kod. Na kraju, budući da se mnogi dobri i pouzdani kodovi mogu se dizajnirati pomoću ranije konstruiranih kodova, u petom poglavlju opisane su metode kojima se to može postići i koje se u praksi dosta često koriste.
Abstract (english)
Today’s world is more than ever world of information so we can expect that the need for most efficient and reliable transmission of those informations will only increase. Coding theory will play very important role in it. This work describes a brief introduction in this dicipline. If one wants to realize its importance, it is essential to know the principles of the way that work devices that transfer messages and what kind of errors can occur during transmission. In the first chapter this issue is explained and the general communication system is described. If we want the transmission of information to be more effective, it is necessary to adapt the amount of code symbols that carry information and the redundancy symbols. Because of that it is important to create good codes. The existence of such codes is a consequence of Shannon’s theorem. To define effective codes it is necessary to add more structure to the code space. This work is focused on linear codes that can be described by generator matrix and parity check matrix. Since all data in computers is stored as binary patterns, it’s not surprising that coding theory pay particular attention to binary codes. One of the most common binary codes that is often used is binary Hammings code. In the end, since many good codes can be created using codes that have already been constructed, few methods that are used to do this are described in chapter 5.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:022370
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-07-10 07:58:46