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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 uu is a deep hole of the standard Reed-Solomon codes [qβˆ’1,k]q[q-1, k]_q if its Lagrange interpolation polynomial is the sum of monomial of degree qβˆ’2q-2 and a polynomial of degree at most kβˆ’1k-1. In this paper, we extend this result by giving a new class of deep holes of the generalized Reed-Solomon codes.Comment: 5 page

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