Hammingovi kodovi ; Hamming Code
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| Název: | Hammingovi kodovi ; Hamming Code |
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| Autoři: | Kocijan, Marta |
| Přispěvatelé: | Mostarac, Nina |
| Informace o vydavateli: | Sveučilište u Rijeci. Fakultet za matematiku. University of Rijeka. Faculty of Mathematics. |
| Rok vydání: | 2025 |
| Sbírka: | Croatian Digital Theses Repository (National and University Library in Zagreb) |
| Témata: | PRIRODNE ZNANOSTI. Matematika. Ostale matematičke discipline, NATURAL SCIENCES. Mathematics. Other Mathematical Disciplines, Binaran linearan kod, Hammingov kod, paritetna matrica, savršen kod, sindrom, Binary linear code, Hamming code, parity-check matrix, perfect code, syndrome |
| Popis: | U ovom radu opisana je vrsta binarnog linearnog koda – Hammingov kod. Nakon ponovljenih osnovnih definicija, uvedena je važna familija kodova, familija linearnih kodova. Kratko su opisani parametri kojima možemo opisati kod, neka svojstva linearnog koda, način zadavanja koda te kako kod detektira grešku pomoću sindroma. U nastavku rada detaljnije se opisuje binaran linearan Hammingov kod. U nekoliko primjera prikazana su i opisana dva načina kodiranja i dekodiranja ovim kodom, pomoću zadane formule i pomoću generirajuće matrice koda. Zatim su navedene neke familije kodova kojima Hammingov kod pripada te je pokazano da pripada savršenim kodovima. Također je spomenuta primjena Hammingovog koda u otkrivanju i ispravljanju pogrešaka u digitalnim komunikacijskim sustavima. ; This paper describes a type of binary linear code – the Hamming code. After revisiting basic definitions, an important family of codes, the family of linear codes, is introduced. The code parameters, key properties, methods of code definition, and the use of syndrome for error detection are explained. The paper focuses in more detail on the binary linear Hamming code. Through several examples, two methods of encoding and decoding are presented and explained, one using a given formula and the other using a generator matrix. Several code families to which the Hamming code belongs are mentioned, and it is shown that it is a perfect code. The application of the Hamming code in detecting and correcting errors in digital communication systems is also presented. |
| Druh dokumentu: | master thesis |
| Popis souboru: | application/pdf |
| Jazyk: | Croatian |
| Relation: | https://zir.nsk.hr/islandora/object/mathri:341; https://urn.nsk.hr/urn:nbn:hr:196:831281; https://www.unirepository.svkri.uniri.hr/islandora/object/mathri:341; https://www.unirepository.svkri.uniri.hr/islandora/object/mathri:341/datastream/PDF |
| Dostupnost: | https://zir.nsk.hr/islandora/object/mathri:341 https://urn.nsk.hr/urn:nbn:hr:196:831281 https://www.unirepository.svkri.uniri.hr/islandora/object/mathri:341 https://www.unirepository.svkri.uniri.hr/islandora/object/mathri:341/datastream/PDF |
| Rights: | http://rightsstatements.org/vocab/InC/1.0/ ; info:eu-repo/semantics/openAccess |
| Přístupové číslo: | edsbas.15970002 |
| Databáze: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | U ovom radu opisana je vrsta binarnog linearnog koda – Hammingov kod. Nakon ponovljenih osnovnih definicija, uvedena je važna familija kodova, familija linearnih kodova. Kratko su opisani parametri kojima možemo opisati kod, neka svojstva linearnog koda, način zadavanja koda te kako kod detektira grešku pomoću sindroma. U nastavku rada detaljnije se opisuje binaran linearan Hammingov kod. U nekoliko primjera prikazana su i opisana dva načina kodiranja i dekodiranja ovim kodom, pomoću zadane formule i pomoću generirajuće matrice koda. Zatim su navedene neke familije kodova kojima Hammingov kod pripada te je pokazano da pripada savršenim kodovima. Također je spomenuta primjena Hammingovog koda u otkrivanju i ispravljanju pogrešaka u digitalnim komunikacijskim sustavima. ; This paper describes a type of binary linear code – the Hamming code. After revisiting basic definitions, an important family of codes, the family of linear codes, is introduced. The code parameters, key properties, methods of code definition, and the use of syndrome for error detection are explained. The paper focuses in more detail on the binary linear Hamming code. Through several examples, two methods of encoding and decoding are presented and explained, one using a given formula and the other using a generator matrix. Several code families to which the Hamming code belongs are mentioned, and it is shown that it is a perfect code. The application of the Hamming code in detecting and correcting errors in digital communication systems is also presented. |
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