Deep holes and MDS extensions of Reed-Solomon codes
Information Theory
2016-12-19 v1 Combinatorics
math.IT
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 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.
Cite
@article{arxiv.1612.05447,
title = {Deep holes and MDS extensions of Reed-Solomon codes},
author = {Krishna Kaipa},
journal= {arXiv preprint arXiv:1612.05447},
year = {2016}
}