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<title><string language="fre"><![CDATA[1.6. Decoding (A Difficult Problem)]]></string></title>
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<string language="fre"><![CDATA[The process of correcting
errors and obtaining back the message is called
decoding. In this sequence, we will focus on this process, the decoding. We would like that the
decoder of the received vector, which is the encoding of
the original message plus a certain vector, is again the
original message, for every message and every
reasonable noisy pattern. The basis of decoding is the
following principle, called Minimum Distance Decoding.
Given a received vector, we look for a codeword that
minimizes the Hamming distance with the received vector One of the most obvious
decoding algorithms is Brute Force. What do we have to do? First of all, enumerate all
codewords until we find one at distance t or less
from the received vector. And we return such codeword. The complexity of this
Brute Force is n*q^k since we have to compare the
received vectors, and all the codewords; recall that
we have q^k codewords. Thus, large
parameters make any Brute Force method impractical. Let us explain a decoding
method using parity check matrices. A vector is in the code if
an only if this product is 0.]]></string></description>
<keyword><string language="fre"><![CDATA[algèbre linéaire]]></string></keyword><keyword><string language="fre"><![CDATA[chiffrement à clé publique]]></string></keyword><keyword><string language="fre"><![CDATA[cryptage des données]]></string></keyword><keyword><string language="fre"><![CDATA[cryptographie]]></string></keyword>
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<date><dateTime>2015-05-05</dateTime></date>
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<string language="fre"><![CDATA[Droits réservés à l'éditeur et aux auteurs. 
Ces ressources de cours sont, sauf mention contraire, diffusées sous Licence Creative Commons. L’utilisateur doit mentionner le nom de l’auteur, il peut exploiter l’œuvre sauf dans un contexte commercial et il ne peut apporter de modifications à l’œuvre originale.]]></string>
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<string language="fre"><![CDATA[1: Error-Correcting Codes and Cryptography]]></string>
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