Extending arcs: an elementary proof.

Alderson, T.

Displaying similar documents to “Extending arcs: an elementary proof.”

A geometrical characterization of the projective plane of order $4$

Andrzej Lewandowski, Hanna Makowiecka (1979)

Časopis pro pěstování matematiky

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A class of complete arcs in multiply derived planes.

Bonisoli, A., Rinaldi, G. (2003)

Advances in Geometry

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On the non-existence of certain hyperovals in dual André planes of order 2 $^{2 h}$ .

Aguglia, Angela, Giuzzi, Luca (2008)

The Electronic Journal of Combinatorics [electronic only]

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The Nonexistence of some Griesmer Arcs in PG(4, 5)

Landjev, Ivan, Rousseva, Assia (2008)

Serdica Journal of Computing

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In this paper, we prove the nonexistence of arcs with parameters (232, 48) and (233, 48) in PG(4,5). This rules out the existence of linear codes with parameters [232,5,184] and [233,5,185] over the field with five elements and improves two instances in the recent tables by Maruta, Shinohara and Kikui of optimal codes of dimension 5 over F5.

A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

Hamada, Noboru, Maruta, Tatsuya, Oya, Yusuke (2012)

Serdica Journal of Computing

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ACM Computing Classification System (1998): E.4. Let q be a prime or a prime power ≥ 3. The purpose of this paper is to give a necessary and sufficient condition for the existence of an (n, r)-arc in PG(2, q ) for given integers n, r and q using the geometric structure of points and lines in PG(2, q ) for n > r ≥ 3. Using the geometric method and a computer, it is shown that there exists no (34, 3) arc in PG(2, 17), equivalently, there exists no [34, 3, 31] 17 code. ...