- Author
- Daniele Bartoli (UGent) , Massimo Giulietti and Giovanni Zini
- Organization
- Abstract
- Complete (k, 3)-arcs in projective planes over finite fields are the geometric counterpart of linear non-extendible Near MDS codes of length k and dimension 3. A class of infinite families of complete (k, 3)-arcs in PG(2, q) is constructed, for q a power of an odd prime p equivalent to 2(mod 3). The order of magnitude of k is smaller than q. This property significantly distinguishes the complete (k, 3)-arcs of this paper from the previously known infinite families, whose size differs from q by at most 2 root q.
- Keywords
- NMDS codes, (k_3)-arcs, Quartic curves, FINITE PROJECTIVE SPACES, ELLIPTIC-CURVES, PACKING PROBLEM, CODING THEORY, FIELDS, STATISTICS, CODES, ARCS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-6843851
- MLA
- Bartoli, Daniele, et al. “Complete (k,3)-Arcs from Quartic Curves.” DESIGNS CODES AND CRYPTOGRAPHY, vol. 79, no. 3, 2016, pp. 487–505, doi:10.1007/s10623-015-0073-7.
- APA
- Bartoli, D., Giulietti, M., & Zini, G. (2016). Complete (k,3)-arcs from quartic curves. DESIGNS CODES AND CRYPTOGRAPHY, 79(3), 487–505. https://doi.org/10.1007/s10623-015-0073-7
- Chicago author-date
- Bartoli, Daniele, Massimo Giulietti, and Giovanni Zini. 2016. “Complete (k,3)-Arcs from Quartic Curves.” DESIGNS CODES AND CRYPTOGRAPHY 79 (3): 487–505. https://doi.org/10.1007/s10623-015-0073-7.
- Chicago author-date (all authors)
- Bartoli, Daniele, Massimo Giulietti, and Giovanni Zini. 2016. “Complete (k,3)-Arcs from Quartic Curves.” DESIGNS CODES AND CRYPTOGRAPHY 79 (3): 487–505. doi:10.1007/s10623-015-0073-7.
- Vancouver
- 1.Bartoli D, Giulietti M, Zini G. Complete (k,3)-arcs from quartic curves. DESIGNS CODES AND CRYPTOGRAPHY. 2016;79(3):487–505.
- IEEE
- [1]D. Bartoli, M. Giulietti, and G. Zini, “Complete (k,3)-arcs from quartic curves,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 79, no. 3, pp. 487–505, 2016.
@article{6843851,
abstract = {{Complete (k, 3)-arcs in projective planes over finite fields are the geometric counterpart of linear non-extendible Near MDS codes of length k and dimension 3. A class of infinite families of complete (k, 3)-arcs in PG(2, q) is constructed, for q a power of an odd prime p equivalent to 2(mod 3). The order of magnitude of k is smaller than q. This property significantly distinguishes the complete (k, 3)-arcs of this paper from the previously known infinite families, whose size differs from q by at most 2 root q.}},
author = {{Bartoli, Daniele and Giulietti, Massimo and Zini, Giovanni}},
issn = {{0925-1022}},
journal = {{DESIGNS CODES AND CRYPTOGRAPHY}},
keywords = {{NMDS codes,(k_3)-arcs,Quartic curves,FINITE PROJECTIVE SPACES,ELLIPTIC-CURVES,PACKING PROBLEM,CODING THEORY,FIELDS,STATISTICS,CODES,ARCS}},
language = {{eng}},
number = {{3}},
pages = {{487--505}},
title = {{Complete (k,3)-arcs from quartic curves}},
url = {{http://doi.org/10.1007/s10623-015-0073-7}},
volume = {{79}},
year = {{2016}},
}
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