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master's thesis
Kodiranje koje ispravlja greške
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:310663
Gaurina, Šime
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Gaurina, Š. (2023). Kodiranje koje ispravlja greške (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:310663

Gaurina, Šime. "Kodiranje koje ispravlja greške." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:310663

Gaurina, Šime. "Kodiranje koje ispravlja greške." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:310663

Gaurina, Š. (2023). 'Kodiranje koje ispravlja greške', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:310663

Gaurina Š. Kodiranje koje ispravlja greške [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:310663

Š. Gaurina, "Kodiranje koje ispravlja greške", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:310663

Metadata
TitleKodiranje koje ispravlja greške
Title (english)Error correcting coding
AuthorŠime Gaurina
MentorFilip Najman (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberZvonimir Bujanović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovoga rada je opisati kodiranja koja ispravljaju greške. U prvom poglavlju su opisani osnovni pojmovi kod kodiranja koja ispravljaju greške i dan je jedan jednostavni primjer kodiranja. U drugom poglavlju se opisuje Hammingov (7, 4) kod i definira se Hammingova udaljenost. U trećem poglavlju opisuju se blok kodovi, tj. kodovi u kojima se podatci dijele na blokove. Također je dana gornja granica na broj kodnih riječi. Opisani su savršeni kodovi i definiran pojam ekvivalentnosti kodova. Opisan je i Hammingov (8, 4) kod koji detektira dvije pogreške u prijenosu poruke. U četvrtom poglavlju su opisani linearni kodovi i dana je definicija dviju važnih matrica: generirajuće matrice i matrice provjere pariteta. Opisano je kako pomoću njih dobiti enkodiranu riječ, odnosno kako provjeriti pripada li riječ kodu. U istom poglavlju su opisane i neke metode dekodiranja poruke. U petom poglavlju se formaliziraju Hammingovi kodovi. Opisani su i simpleks kodovi te Hadamardovi kodovi.
Abstract (english)
The goal of this paper is to describe error-correcting codes. In the first chapter, the basic concepts of error-correcting codes are described and a simple example is given. In the second chapter, the Hamming (7, 4) code is described and the Hamming distance is defined. In the third chapter, block codes are described, i.e. codes in which data is divided into blocks. In the same chapter, the upper limit for the number of codewords is given. Perfect codes are described and the concept of code equivalence is defined. The Hamming (8, 4) code, which detects two errors in message transmission is described. In the fourth chapter, linear codes are described and two important matrices are defined: generator matrix and parity check matrix. It is described how to use them to encode a word and how to check whether the word belongs to the code. In the same chapter, some methods of message decoding are described. In the fifth chapter, Hamming codes are formalized. Simplex codes and Hadamard codes are also described.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:310663
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-03-27 07:45:30