Y.S.Han RS Codes 1 Reed-Solomon Codes Construction (1) The first construction of Reed-solomon (RS)codes is simply to evaluate the information polynomials at all the non-zero elements of finite field GF(gm). Let a be a primitive element in GF(gm)and let n=gm-1. .Let u(x)=uo+u+.+u-1 be the information polynomial,where u∈GF(qm)for all0≤i≤k-l. The encoding is defined by the mapping p:u(x)>by (0,v1,…,n-1）=(u(1,u(a,u(a2),,u(an-1). The RS code of length n and dimensional k over GF(gm) is the image under all polynomials in GF(g")[x]of School of Electrical Engineering Intelligentization,Dongguan University of Technology Y. S. Han RS Codes 1 Reed-Solomon Codes Construction (1) • The first construction of Reed-solomon (RS) codes is simply to evaluate the information polynomials at all the non-zero elements of finite field GF(q m). • Let α be a primitive element in GF(q m) and let n = q m − 1. • Let u(x) = u0 + u1 x + · · · + uk−1 x k−1 be the information polynomial, where ui ∈ GF(q m) for all 0 ≤ i ≤ k − 1. • The encoding is defined by the mapping ρ : u(x) −→ v by (v0, v1, . . . , vn−1 ) = (u(1), u(α), u(α 2 ), . . . , u(α n−1 )). • The RS code of length n and dimensional k over GF(q m) is the image under all polynomials in GF(q m)[x] of School of Electrical Engineering & Intelligentization, Dongguan University of Technology