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

Suppose the received word is
(R(x 1 );R(x 2 );:::;R(x N ))
At the receiver, N equations can be formed, some
of which are wrong if there are transmission errors.
R(0) = m 1
R() = m 1 + m 2 + m 3 2 + +m M M,1
R( 2 ) = m 1 +m 2 +m 3 22 ++m M 2(M,1)
.
R(1) = m 1 + m 2 + m 3 + +m M
Any M of these equations have full rank and can
be solved. By trying many sets of M equations,
the correct answer will appear more often than any
wrong answer provided the number of errors is less
than (2 n , M +1)=2.
Choosing M equations and solving those equations
is equivalent to Lagrange interpolation.
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