"When ???t??? is odd, the system represents the roots ri of the error locator polynomial as a linear combination of ri,k??k for k=0,1 . . . m???1, where ri,k??GF(2) and ??k is an element of a dual basis for GF(2m) over GF(2), and Tr(??j??k) equals one when j=k and equals zero when jk." . . . .