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

Not all of the e's are non-zero.
Let E be the set of indices for which e i 6=0
Dene
Q S (Z) =
Y
i2E\S
(Z,x i )
and
Q C (Z) =
Y
i2E\S c (Z,x i )
The roots of Q S (Z) are those x i for which i 2 S
and e i 6= 0 While the roots of Q C (Z) are those x i
for which i 2 S c and e i 6=0
The summation expression in the syndrome equations
can now be put over a common denominator
to give
k = e k , A(x k)
Q S (x k )
where the degree of Q S is the number of errors at
selected indices and the degree of A is less
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