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<title><string language="fre"><![CDATA[4.3. Distinguisher for GRS codes]]></string></title>
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<string language="fre"><![CDATA[In this session we will see
that generalized Reed-Solomon codes behave differently than random
codes with respect to the star operation. Thus we can define a distinguisher
for Generalized Reed-Solomon codes. Let us recall the definition of
Generalized Reed-Solomon codes. We will need an n-tuple of
mutually distinct elements of Fq. We need a vector b which is
an n-tuple of nonzero elements of Fq. We need
to define the vector space of all polynomials of degree
at most k and we also need to define a evaluation map. Then
the Generalized Reed-Solomon codes of dimension k,
associated with a pair (a,b) is the evaluation of all polynomials of
degree at most k at the pair (a,b). The element a is called
code locator and the element b is called the column multiplier. Let us see some properties of
Generalized Reed-Solomon codes. The Generalized Reed-Solomon
codes is an MDS code that is its error correction
performance is optimal. Moreover, the dual of a
Generalized Reed-Solomon code is also a Generalized
Reed-Solomon code, in particular the dual of a Generalized
Reed-Solomon code of dimension k defined by the pair (a,b)
is a Generalized Reed-Solomon code of dimension n-k
defined by the same code locator but some non zero vector b.]]></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><keyword><string language="fre"><![CDATA[code correcteur]]></string></keyword><keyword><string language="fre"><![CDATA[algorithmes]]></string></keyword><keyword><string language="fre"><![CDATA[GRS code]]></string></keyword>
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<date><dateTime>2015-05-05</dateTime></date>
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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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