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On the covering radius of MDS codes

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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 root 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 root q, these are the shortest q-ary MDS codes with covering radius r - 1.
Keywords
PLANE ARCS, SMALL COMPLETE CAPS, ELLIPTIC-CURVES, COMPLETENESS, SPACES, MDS codes, AG codes, covering radius

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Please use this url to cite or link to this publication:

MLA
Bartoli, Daniele, Massimo Giulietti, and Irene Platoni. “On the Covering Radius of MDS Codes.” IEEE TRANSACTIONS ON INFORMATION THEORY 61.2 (2015): 801–811. Print.
APA
Bartoli, D., Giulietti, M., & Platoni, I. (2015). On the covering radius of MDS codes. IEEE TRANSACTIONS ON INFORMATION THEORY, 61(2), 801–811.
Chicago author-date
Bartoli, Daniele, Massimo Giulietti, and Irene Platoni. 2015. “On the Covering Radius of MDS Codes.” Ieee Transactions on Information Theory 61 (2): 801–811.
Chicago author-date (all authors)
Bartoli, Daniele, Massimo Giulietti, and Irene Platoni. 2015. “On the Covering Radius of MDS Codes.” Ieee Transactions on Information Theory 61 (2): 801–811.
Vancouver
1.
Bartoli D, Giulietti M, Platoni I. On the covering radius of MDS codes. IEEE TRANSACTIONS ON INFORMATION THEORY. 2015;61(2):801–11.
IEEE
[1]
D. Bartoli, M. Giulietti, and I. Platoni, “On the covering radius of MDS codes,” IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 61, no. 2, pp. 801–811, 2015.
@article{8033703,
  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 root 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 root q, these are the shortest q-ary MDS codes with covering radius r - 1.},
  author       = {Bartoli, Daniele and Giulietti, Massimo and Platoni, Irene},
  issn         = {0018-9448},
  journal      = {IEEE TRANSACTIONS ON INFORMATION THEORY},
  keywords     = {PLANE ARCS,SMALL COMPLETE CAPS,ELLIPTIC-CURVES,COMPLETENESS,SPACES,MDS codes,AG codes,covering radius},
  language     = {eng},
  number       = {2},
  pages        = {801--811},
  title        = {On the covering radius of MDS codes},
  url          = {http://dx.doi.org/10.1109/TIT.2014.2385084},
  volume       = {61},
  year         = {2015},
}

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