Y.S.Han Decoding BCH/RS Codes 3 Syndrome Computation .Let a,a2,.2 be the 2t consecutive roots of the generator polynomial for the BCH/RS code,where a is an element in finite field GF(g")with order n. Let y(z)be the received vector.Then define the syndrome Si,1≤j≤2t,as follows: Sj y(ai)=c(a)+e(ai)=e(ai) n-1 oy (1) U k=1 School of Electrical Engineering Intelligentization,Dongguan University of Technology Y. S. Han Decoding BCH/RS Codes 3 Syndrome Computation • Let α, α2 , . . . , α2t be the 2t consecutive roots of the generator polynomial for the BCH/RS code, where α is an element in finite field GF(q m) with order n. • Let y(x) be the received vector. Then define the syndrome Sj , 1 ≤ j ≤ 2t, as follows: Sj = y(α j ) = c(α j ) + e(α j ) = e(α j ) = n ∑−1 i=0 ei (α j ) i = ∑ v k=1 eik α ikj , (1) School of Electrical Engineering & Intelligentization, Dongguan University of Technology