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<title><string language="fre"><![CDATA[1.3. Encoding (Linear Transformation)]]></string></title>
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<string language="fre"><![CDATA[In this session, we will
talk about the easy map of the
 - one-way trapdoor functions
based on error-correcting codes. We suppose that the set of 
all messages that we wish to transmit is the set of k-tuples having
elements from the field Fq. There are qk possible
messages and we referred to it as the message space.  In order to detect and
possibly correct errors, we add some redundancy, thus the k
tuples will be embedded into n-tuples with n greater than k. In this MOOC, we will focus on linear
encoder that is linear transformations. Every linear transformation can be
represented by a matrix multiplication. Thus our code, which is the
image of the message space,  consists of codewords of the
same length which are closed under addition and
scalar multiplication. If the encoded matrix
is injective, that is, if no two messages have the
same image, or in other words, if the encoding matrix has
rank k, then we consider a one to one correspondence between the
message space and the linear code. These are the cases that
will care, where the encoding is some multiplication by a
matrix of rank k, that is, our code is a vector subspace of Fq^n. ]]></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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<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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