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Complete (k,3)-arcs from quartic curves

(2016) DESIGNS CODES AND CRYPTOGRAPHY. 79(3). p.487-505
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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:

Chicago
Bartoli, Daniele, Massimo Giulietti, and Giovanni Zini. 2016. “Complete (k,3)-arcs from Quartic Curves.” Designs Codes and Cryptography 79 (3): 487–505.
APA
Bartoli, D., Giulietti, M., & Zini, G. (2016). Complete (k,3)-arcs from quartic curves. DESIGNS CODES AND CRYPTOGRAPHY, 79(3), 487–505.
Vancouver
1.
Bartoli D, Giulietti M, Zini G. Complete (k,3)-arcs from quartic curves. DESIGNS CODES AND CRYPTOGRAPHY. 2016;79(3):487–505.
MLA
Bartoli, Daniele, Massimo Giulietti, and Giovanni Zini. “Complete (k,3)-arcs from Quartic Curves.” DESIGNS CODES AND CRYPTOGRAPHY 79.3 (2016): 487–505. Print.
@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},
  keyword      = {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://dx.doi.org/10.1007/s10623-015-0073-7},
  volume       = {79},
  year         = {2016},
}

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