Abstract
We study the problem of classifying deep holes of Reed–Solomon codes. We show that this problem is equivalent to the problem of classifying maximum distance separable (MDS) extensions of Reed–Solomon codes by one digit. This equivalence allows us to improve recent results on the former problem. In particular, we classify deep holes of Reed–Solomon codes of dimension greater than half the alphabet size. We also give a complete classification of deep holes of Reed–Solomon codes with redundancy three in all dimensions.
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