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<title><string language="fre"><![CDATA[1.4. Parity Checking]]></string></title>
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<string language="fre"><![CDATA[ There are two standard
ways to describe a subspace, explicitly by giving a
basis, or implicitly, by the solution space of the set of
homogeneous linear equations. Therefore, there are two
ways of describing a linear code, explicitly, as we
have seen in the previous sequence, by a generator
matrix, or implicitly, by the null space of a matrix. This is
what we will see in this sequence. This leads to the
following definition: H is a parity check matrix of a linear code, if
the code is the null space of H. In this way, any linear code
is completely specified by a
parity check matrix. Suppose that we have a
message of 4 bits, then we put them in the middle of the
Venn Diagram, and we complete the empty three areas
according to the following rules. The number of ones in
every circle is even. This gives us three redundant
bits that we add to the message. We say that our circle is
incorrect, if its parity is odd. So, if you modify any
symbol, then the error is propagated to the circle
where this symbol is involved. Thus, if the circle one and
the second circle are wrong, then we deduce that an error has
occurred in the first position. If the three circles
are wrong, then we deduce that there has been an
error in the fourth position.
Thus, the redundant
information can be obtained from the message by means of three
linear equations or parity check.]]></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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