Journal article
M. Giulietti, F. Pambianco, F. Torres, E. Ughi
Des. Codes Cryptogr., 2000
Des. Codes Cryptogr., 2000
Semantic Scholar
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DOI
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APA
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Giulietti, M., Pambianco, F., Torres, F., & Ughi, E. (2000). On Complete Arcs Arising from Plane Curves. Des. Codes Cryptogr.
Chicago/Turabian
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Giulietti, M., F. Pambianco, F. Torres, and E. Ughi. “On Complete Arcs Arising from Plane Curves.” Des. Codes Cryptogr. (2000).
MLA
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Giulietti, M., et al. “On Complete Arcs Arising from Plane Curves.” Des. Codes Cryptogr., 2000.
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@article{m2000a,
title = {On Complete Arcs Arising from Plane Curves},
year = {2000},
journal = {Des. Codes Cryptogr.},
author = {Giulietti, M. and Pambianco, F. and Torres, F. and Ughi, E.}
}
Abstract
AbstractWe point out an interplay between $$F_q$$ -Frobenius non-classical plane curves and complete $$\left( {k,d} \right)$$ -arcs in $$P^{\text{2}} \left( {F_q } \right)$$ . A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete $$\left( {k,d} \right)$$ -arcs with parameters $$k = d\left( {q - d + 2} \right)$$ and $$d = \left( {q - 1} \right)/\left( {q\prime - 1} \right),q\prime$$ being a power of the characteristic. In addition, for q a square, new complete $$\left( {k,d} \right)$$ -arcs with either $$k = q\sqrt q b + 1$$ and $$d = \left( {\sqrt q + 1} \right)b\left( {2 \leqslant b \leqslant \sqrt q - 1} \right)$$ or $$k = \left( {q - 1} \right)\sqrt q b + \sqrt q + 1$$ and $$d = \left( {\sqrt q + 1} \right)b\left( {2 \leqslant b \leqslant \sqrt q - 2} \right)$$ are constructed by using certain reducible plane curves.
