## 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 gener
The automorphism group of a complete (q − 1)-arc in PG(2,q)
✍ Scribed by A. H. Ali; J. W. P. Hirschfeld; H. Kaneta
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 698 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
✦ Synopsis
The automorphism group of the set of 12 points associated with an apolar system of conics is determined. A complete (q -&arc for q = 13 can be obtained as a special case. The orbits of its automorphism group are also described. 0 I Y Y ~ John Wile?. & Sons, h e .
📜 SIMILAR VOLUMES
Two results are proved: (1) In PG(3, q), q=2 h, h>~3, every q3-arc can be uniquely completed to a (q + 1)3-arc. (2) In PG(4, q), q = 2", h ~> 3, every (q + 1)4-arc is a normal rational curve. ## 1. In~oduction We assume throughout this paper that the base field GF(q) is of order q = 2 h, where h i
## Abstract Some new families of small complete caps in __PG__(__N, q__), __q__ even, are described. By using inductive arguments, the problem of the construction of small complete caps in projective spaces of arbitrary dimensions is reduced to the same problem in the plane. The caps constructed in
## Abstract Based on the classification of superregular matrices, the numbers of non‐equivalent __n__‐arcs and complete __n__‐arcs in PG(__r__, __q__) are determined (i) for 4 ≤ __q__ ≤ 19, 2 ≤ __r__ ≤ q − 2 and arbitrary __n__, (ii) for 23 ≤ __q__ ≤ 32, __r__ = 2 and __n__ ≥ q − 8<$>. The equivale