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The complete (k, 3)-arcs of PG(2,q), q≤13

✍ Scribed by K. Coolsaet; H. Sticker

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
197 KB
Volume
20
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

We have classified by computer the projectively distinct complete (k, 3)‐arcs in PG(2, q), q≤13. The algorithm used is an application of isomorph‐free backtracking using canonical augmentation, an adaptation of our earlier algorithms for the generation of (k, 2)‐arcs. We describe those parts of the algorithms which are specific to the particular problem of (k, 3)‐arcs. For each of these arcs we have also determined the automorphism group. The results are summarized in tables where the arcs are listed according to size and automorphism group. For the arcs with the larger automorphism groups, explicit descriptions are given. Part of the computer results can be generalized to other values of q: we describe constructions of arcs having S~4~ as a group of automorphisms, arcs containing the union of three “half conics” and arcs constructed from parts of cubic curves. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 20:89‐111, 2012

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