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Title:VEKTORSKI PROSTORI LINEARNIH KOD
Authors:ID Frajzman, Valentina (Author)
ID Banič, Iztok (Mentor) More about this mentor... New window
Files:.pdf UNI_Frajzman_Valentina_2013.pdf (826,29 KB)
MD5: 822B9B86CA038DEBDCB2E420692F562F
PID: 20.500.12556/dkum/759bd0b3-5ad7-4238-bf14-b77758a5749c
 
Language:Slovenian
Work type:Undergraduate thesis
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Kode za odpravljanje napak nam pomagajo pri popravkih v motnjah prenosa ali hranjenja podatkov. Ponavadi je koda v binarnem zapisu. Sestavljena je iz zaporedja 0 in 1. Ker so bile kode premalo natancne so dodali vsakemu sporocilu dodaten bit. Živimo v dobi katere bistveno ozadje je tehnologija, zato imajo kode, ki popravljajo napake zelo veliko vlogo. Uporaba paritetnega bita v mehanizmu zaznavanja napak je ena najbolj preprostih in znanih shem v racunalništvu. Pri popravljanju napak govorimo tudi o Hammingovih kodah in linearnih kodah. Pri Hammingovih kodah se izkažeta za pomembna pojma Hammingova razdalja in Hammingova teža. Algebraicna struktura linearnih kod podaja okvir za ucinkovite algoritme za kodiranje in dekodiranje. Večina aktualnih kod za popravljanje napak spada v podskupine linearnih kod.
Keywords:Hamming-ova koda, vektor, vektorski prostor, krogla, linearna koda, popolna koda, generatorska matrika, paritetna matrika
Place of publishing:Maribor
Publisher:[V. Frajzman]
Year of publishing:2013
PID:20.500.12556/DKUM-39334 New window
UDC:51(043.2)
COBISS.SI-ID:20076040 New window
NUK URN:URN:SI:UM:DK:NTLFUXWQ
Publication date in DKUM:24.09.2013
Views:1643
Downloads:127
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:VECTOR SPACES OF LINEAR CODES
Abstract:Error Correcting Codes help us with correcting errors in transmission or storage of data. Usually the code is in a binary format. It consists of a sequence of 0 and 1. Since the codes were not accurate enough, each message got an extra bit. We live in the age of technology, where the codes correcting errors play an important role. Using the parity bit in the error detection mechanism is one of the most simple and well-known schemes in computer science. We are talking about the Hamming codes and linear codes when we are correcting errors. The Hamming distance and Hamming weight prove to be an important concept with the Hamming codes. Algebraic structure of linear codes provides a framework for efficient algorithms for encoding and decoding. Most current codes for error correction belong to the subgroup of linear codes.
Keywords:Hamming code, vector, vector space, sphere, linear code, perfect code, generator matrix, dual code, parity-check matrix


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