A new proof of the existence of (q2−q + 1)-arcs inpg(2, q2)
✍ Scribed by Antonio Cossidente
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 58 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0047-2468
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📜 SIMILAR VOLUMES
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 .
## 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
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
It is unknown whether or not there exists an [87, 5, 57 ; 31-code. Such a code would meet the Griesmer bound. The purpose of this paper is to give a constructive proof of the existence of [q4 + q2 \_ q, 5, q'\* -q3 + q2 \_ 2q; q]-codes for any prime power q \_> 3. As a special case, it is shown that