Y.S.Han RS Codes 6 Weight Distributions for RS Codes A code is called maximum distance separable (MDS)code when its dmin is equal to n-k+1.A family of well-known MDS nonbinary codes is Reed-Solomon codes. The dual code of any (n,k)MDS code C is also an (n,n-k)MDS code with dmin =k +1. It can be proved as follows:We need to prove that the (n,n-k)dual code C,which is generated by the parity-check matrix H of C,has dmin =k+1.Let c∈C-have weight w,0<w≤k.Since w≤k,there are at least n-k coordinates of c are zero.Let HIs be an (n-k)x(n-k)submatrix formed by any collection of n-k columns of II in the above coordinates.Since the School of Electrical Engineering Intelligentization,Dongguan University of TechnologyY. S. Han RS Codes 6 Weight Distributions for RS Codes • A code is called maximum distance separable (MDS) code when its dmin is equal to n − k + 1. A family of well-known MDS nonbinary codes is Reed-Solomon codes. • The dual code of any (n, k) MDS code C is also an (n, n − k) MDS code with dmin = k + 1. • It can be proved as follows: We need to prove that the (n, n − k) dual code C⊥ , which is generated by the parity-check matrix H of C, has dmin = k + 1. Let c ∈ C⊥ have weight w, 0 < w ≤ k. Since w ≤ k, there are at least n − k coordinates of c are zero. Let Hs be an (n − k) × (n − k) submatrix formed by any collection of n − k columns of H in the above coordinates. Since the School of Electrical Engineering & Intelligentization, Dongguan University of Technology