Journal article
D. Bartoli, M. Giulietti, Irene Platoni
IEEE Transactions on Information Theory, 2015
IEEE Transactions on Information Theory, 2015
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APA
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Bartoli, D., Giulietti, M., & Platoni, I. (2015). On the Covering Radius of MDS Codes. IEEE Transactions on Information Theory.
Chicago/Turabian
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Bartoli, D., M. Giulietti, and Irene Platoni. “On the Covering Radius of MDS Codes.” IEEE Transactions on Information Theory (2015).
MLA
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Bartoli, D., et al. “On the Covering Radius of MDS Codes.” IEEE Transactions on Information Theory, 2015.
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@article{d2015a,
title = {On the Covering Radius of MDS Codes},
year = {2015},
journal = {IEEE Transactions on Information Theory},
author = {Bartoli, D. and Giulietti, M. and Platoni, Irene}
}
Abstract
For a linear maximum distance separable (MDS) code with redundancy r, the covering radius is either r or r -1. However, for r > 3, few examples of q-ary linear MDS codes with radius r -1 are known, including the Reed-Solomon codes with length q + 1. In this paper, for redundancies r as large as 12√q, infinite families of q-ary MDS codes with covering radius r - 1 and length less than q + 1 are constructed. These codes are obtained from algebraic-geometric codes arising from elliptic curves. For most pairs (r, q) with r ≤ 12√q, these are the shortest q-ary MDS codes with covering radius r - 1.