The classification of $(42,6)_8$ arcs

Anton Betten; Eun Ju Cheon; Seon Jeong Kim; Tatsuya Maruta

doi:10.3934/amc.2011.5.209

Article Contents

2011, Volume 5, Issue 2: 209-223. Doi: 10.3934/amc.2011.5.209

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The classification of $(42,6)_8$ arcs

1.
Department of Mathematics, Colorado State University, Fort Collins, CO 80523
2.
Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701
3.
Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531

Received: March 31, 2010

Revised: September 30, 2010

Published: April 2011

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Abstract

It is known that $42$ is the largest size of a $6$-arc in the Desarguesian projective plane of order $8$. In this paper, we classify these $(42,6)_8$ arcs. Equivalently, we classify the smallest $3$-fold blocking sets in PG$(2,8)$, which have size $31$.

Keywords:

Arc,
blocking set,
projective plane.

Mathematics Subject Classification: Primary: 51E21; Secondary: 05E18.

Citation:

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References

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