AIMS Mathematics, 2016, 1(2): 96-101. doi: 10.3934/Math.2016.2.96.

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On deep holes of generalized Reed-Solomon codes

Mathematical College, Sichuan University, Chengdu 610064, P.R. China

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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Keywords Deep hole; error distance; standard Reed-Solomon code; generalized Reed-Solomon code; Lagrange interpolation polynomial

Citation: Shaofang Hong, Rongjun Wu. On deep holes of generalized Reed-Solomon codes. AIMS Mathematics, 2016, 1(2): 96-101. doi: 10.3934/Math.2016.2.96


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