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

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Initialization: J 0 =0; Q 0 (Z)=1;P 0 (Z)=0;W 0 (Z)=1;V 0 (Z)=1 Since k = 0, there are no equations to verify. 22
When we have generated Q k ;P k ;W k ;V k we will have two solutions to the rst k equations. (Q k ;P k ) and (W k ;V k ) However the pair (W k ;V k ) will be "less suitable" than (Q k ;P k ) in a certain sense. But the pair will be useful in constructing (Q k+1 ;P k+1 ) 23
Page 1 and 2: L.R.Welch THE ORIGINAL VIEW OF REED
Page 3 and 4: MATHEMATICALLY: Let (x 1 ;x 2 ;;x N
Page 5 and 6: THE CLASSICAL VIEW Reed Solomon Cod
Page 7 and 8: Alternatively, dividing Z N ,M P (Z
Page 9 and 10: An alternative is to form a codewor
Page 11 and 12: Later Berlekamp found a faster algo
Page 13 and 14: LAGRANGE INTERPOLATION For each i 2
Page 15 and 16: Subtracting the interpolated values
Page 17 and 18: The syndromes can now be expressed
Page 19 and 20: For k 2 S c , either e k =0orQ C (x
Page 21: We introduce an auxillary pair of p
Page 25 and 26: IF d k 6=0 We form another quantity
Page 27 and 28: IF d k =0 0 B @ Q k(Z) P k (Z) W k
Page 29 and 30: WHAT ABOUT MINIMALITY This is the d
Page 31 and 32: THEOREM: The algorithm described ab
Page 33 and 34: Lemmas 5,6 L(Q k (Z);P k (Z)) + L(W

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

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