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arXiv · 1205.7016

On deep holes of generalized Reed-Solomon codes

Shaofang Hong·Rongjun Wu
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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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Shaofang Hong, Rongjun Wu. 2012-05-31. On deep holes of generalized Reed-Solomon codes. https://doi.org/10.3934/math.2016.2.96

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