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

CLASSICAL DECODING
[W.W. Peterson, IRE IT-6 Sept 1960]
Receive (r 1 ;r 2 ;;r N )
and form
R(Z) =
C( i ) = 0
N X
i=1
r i Z i,1
= C(Z)+E(Z)
S i = R( i ) = E( i )
for 1 i N , M
for 1 i N , M
Peterson observed that the S i satisfy a linear recursion.
0= e X
i=0
q i S k+i
for 1 k N , M , e
where Q(Z) = P e
i=0
q i Z i has the error locations as
its roots.
This gives a simple system of linear equations to
nd the error locations. Another system solves for
the error values.
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