Error distance of standard Reed-Solomon codes

Abstract:

Error distance plays an important role in the decoding of standard Reed-Solomon codes. In 2012, Hong and Wu proposed a famous conjecture of standard Reed-Solomon codes on error distance. In this paper, We show that some polynomials of degree $q-4$ can not define deep holes over finite fields with odd characteristic by using the quadratic form and the generator matrix of maximum distance separable codes. In fact, we partially proved error distance conjecture of standard Reed-Solomon codes.