On deep holes of generalized Reed-Solomon codes

Abstract

Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q-1, k]q if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. In this paper, we extend this result by giving a new class of deep holes of the generalized Reed-Solomon codes.

Keywords

• Deep hole| error distance| standard Reed-Solomon code| generalized Reed-Solomon code| Lagrange interpolation polynomial