A remark on ordinary codewords of standard Reed-Solomon codes

Reed-Solomon codes are now widely used in digital communication,which are an important class of linear codes.The maximum likelihood decoding algorithm(MLD)is usually used in the decoding process of Reed-Solomon codes.For the received word u∈Fq,MLD algorithm lies in determining its error distance d(u,C).It is well-known that d(u,C)n-degu(x),where u(x)is the Lagrange interpolation polynomial of u.If d(u,C)=n-degu(x),then uis called an ordinary codeword of C.For standard Reed-Solomon code,determine the ordinary codeword is an open problem.In this paper,the authors proved one class ordinary codeword of standard Reed-Solomon codes by computing the number of roots of specific equation.