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A full classification of the complete k ‐arcs of PG(2,23) and PG(2,25) by K. Coolsaet; H. Sticker is a Engineering article available to read on EtoBox.

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## Abstract A full classification (up to equivalence) of all complete __k__‐arcs in the Desarguesian projective planes of order 23 and 25 was obtained by computer. The algorithm used is an application of isomorph‐free backtracking using canonical augmentation, as introduced by McKay, which we have adapted to the case of subset generation in Desarguesian projective planes. We have applied two variants of the same algorithm, and both techniques yield exactly the same results. Earlier (partial) results by other authors on __k__‐arcs in PG(2, __q__) with __q__⩽25, are reproduced by our programs. We describe those parts of the algorithms which are relevant to the particular problem of generating __k__‐arcs and which have made this project feasible. We also list the number of complete arcs in PG(2, 23) and PG(2, 25) according to size of the arc and type of the automorphism group. Explicit descriptions are given for the arcs with the larger automorphism groups. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 459–477, 2009

Who reads A full classification of the complete k ‐arcs of PG(2,23) and PG(2,25)?

Author

K. Coolsaet; H. Sticker

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1063-8539)

Published

2009

Language

EN

Field

Engineering (Physical Sciences)