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On deep holes of generalized Reed-Solomon codes
Published 31 May 2012 in math.NT, cs.IT, and math.IT | (1205.7016v2)
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.
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