THE ORIGINAL VIEW OF REED-SOLOMON CODES THE ORIGINAL ...

INTERPOLATION POLYNOMIALS
Given S, the 's are constructed as follows:
Let
G(Z) = Y (Z,x j )
j2S
and let G 0 (Z) be its formal derivative.
Then
i (Z) =
G(Z)
(Z,x i )G 0 (x i )
It is clear that i (x j ) = 0 for i; j 2 S and
j 6= i. That i (x i ) = 1 follows from the rule of
L'Hospital which isvalid for ratios of polynomials
over any eld.
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