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

STEP k
At the beginning of step k we have
J k,1 and
Q k,1 (Z);P k,1 (Z);W k,1 (Z);V k,1 (Z)
We form
d k = Q k,1 (x k ) k , P k,1 (x k )
IF d k =0
J k = J k,1 +1
Q k (Z) = Q k,1 (Z)
P k (Z) = P k,1 (Z)
W k (Z) = (Z,x k )W k,1 (Z)
V k (Z) = (Z,x k )V k,1 (Z)
In this case
(Q k,1 ;P k,1 )
already satisfy the k'th equation
and
multiplication by (Z,x k )
forces the pair
W k (Z);V k (Z)
to satisfy the k'th equation.
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