Y.S.Han RS Codes 3 Reed-Solomon Codes Construction(2) The RS codes can be constructed by finding their generator polynomials. In GF(gm),the minimum polynomial for any element ai is simply (x-a). ·Letg(c)=(x-a)(x-ab+1)…(c-ab+2t-l)be the generator polynomial for the RS code.Since the degree of g(x)is exactly equal to 2t,by the BCH bound, n =qm-1,n-k 2t,and dmin >n-k +1. Again,by the Singleton bound,dmin =n-k+1. Considering GF(8)with the primitive polynomial School of Electrical Engineering Intelligentization,Dongguan University of Technology Y. S. Han RS Codes 3 Reed-Solomon Codes Construction (2) • The RS codes can be constructed by finding their generator polynomials. • In GF(q m), the minimum polynomial for any element α i is simply (x − α i ). • Let g(x) = (x − α b )(x − α b+1)· · ·(x − α b+2t−1 ) be the generator polynomial for the RS code. Since the degree of g(x) is exactly equal to 2t, by the BCH bound, n = q m − 1, n − k = 2t, and dmin ≥ n − k + 1. • Again, by the Singleton bound, dmin = n − k + 1. • Considering GF(8) with the primitive polynomial School of Electrical Engineering & Intelligentization, Dongguan University of Technology