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

MATHEMATICALLY:
Let (x 1 ;x 2 ;;x N )beanenumeration of the
elements of the eld.
Let (m 1 ;m 2 ;;m M ) be a message where
m i 2 GF (2 n ).
Dene a polynomial by
P (Z) =m 1 +m 2 Z+m 3 Z 2 ++m M Z M,1
Then the codeword is
(P (x 1 );P(x 2 );:::;P(x N ))
The enumeration used by Reed and Solomon was
as follows.
Let be a primitive element in GF(2 n ). Then the
enumeration is
(x 1 ;x 2 ;;x N )=(0;; 2 ;; N,2 ;1)
3