Notice
4.3. Distinguisher for GRS codes
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Descriptif
In this session we will seethat generalized Reed-Solomon codes behave differently than randomcodes with respect to the star operation. Thus we can define a distinguisherfor Generalized Reed-Solomon codes. Let us recall the definition ofGeneralized Reed-Solomon codes. We will need an n-tuple ofmutually distinct elements of Fq. We need a vector b which isan n-tuple of nonzero elements of Fq. We needto define the vector space of all polynomials of degreeat most k and we also need to define a evaluation map. Thenthe Generalized Reed-Solomon codes of dimension k,associated with a pair (a,b) is the evaluation of all polynomials ofdegree at most k at the pair (a,b). The element a is calledcode locator and the element b is called the column multiplier. Let us see some properties ofGeneralized Reed-Solomon codes. The Generalized Reed-Solomoncodes is an MDS code that is its error correctionperformance is optimal. Moreover, the dual of aGeneralized Reed-Solomon code is also a GeneralizedReed-Solomon code, in particular the dual of a GeneralizedReed-Solomon code of dimension k defined by the pair (a,b)is a Generalized Reed-Solomon code of dimension n-kdefined by the same code locator but some non zero vector b.
Intervention
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