Y.S.Han RS Codes 8 nonsingular.So,by row reduction on G,any k xk submatrix can be reduced to the k x k identity matrix. The number of codewords in a q-ary (n,k)MDS code C of weight dmin =n-k+1 is 4=g-(n-+) It can be proved as follows:Select an arbitrary set of k coordinates as information positions for an information u of weight 1.The systemic encoding for these coordinates thus has k-1 zeros in it.Since the minimum distance of the code is n-k+1,all the n-k parity check symbols must be nonzero.Since there are(k”）=(n-k+i) School of Electrical Engineering Intelligentization,Dongguan University of TechnologyY. S. Han RS Codes 8 nonsingular. So, by row reduction on G, any k × k submatrix can be reduced to the k × k identity matrix. • The number of codewords in a q-ary (n, k) MDS code C of weight dmin = n − k + 1 is An−k+1 = (q−1)( n n − k + 1) . • It can be proved as follows: Select an arbitrary set of k coordinates as information positions for an information u of weight 1. The systemic encoding for these coordinates thus has k − 1 zeros in it. Since the minimum distance of the code is n − k + 1, all the n − k parity check symbols must be nonzero. Since there are ( n k−1 ) = ( n n−k+1) School of Electrical Engineering & Intelligentization, Dongguan University of Technology