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

IF d k 6=0
We form another quantity,
c k = d ,1
k (W k,1 (x k ) k , V k,1(x k ))
and set
Q k (Z) = (Z , x k )Q k,1 (Z)
P k (Z) = (Z , x k )P k,1 (Z)
W k (Z) = W k,1 , c k Q k,1 (Z)
V k (Z) = V k,1 , c k P k,1 (Z)
It is readily veried that the two
pair of polynomials satisfy the rst
k equations.
HOWEVER, we are not done with this case.
IF J k,1 = 0 then
swap the two pair.
Q k (Z) $ W k (Z)
P k (Z) $ V k (Z)
and set J k =0
OTHERWISE set J k = J k,1 , 1
and do not swap pairs.
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