In this paper it is shown that given a non-degenerate elliptic quadric in the projective space PG(2n -1, q), q odd, then there does not exist a spread of PG(2n -1, q) such that each element of the spread meets the quadric in a maximal totally singular subspace. An immediate consequence is that the c
Maximal arcs and disjoint maximal arcs in projective planes of order 16
β Scribed by Nicholas Hamilton; Stoicho D. Stoichev; Vladimir D. Tonchev
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 601 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0047-2468
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Using maximal arcs in PG(3, 2 m ), we give a new proof of the fact that the binary cyclic code C (m) 1, 2 2h &2 h +1 , the code of length 2 m &1 with defining zeroes : and : t , t=2 2h &2 h +1, where : is a primitive element in GF(2 m ), is 2-error-correcting when gcd(m, h)=1.
We construct by computer all of the hyperovals in the 22 known projective planes of order 16. Our most interesting result is that four of the planes contain no hyperovals, thus providing counterexamples to the old conjecture that every finite projective plane contains an oval.
## Abstract The sporadic complete 12βarc in PG(2, 13) contains eight points from a conic. In PG(2,__q__) with __q__>13 odd, all known complete __k__βarcs sharing exactly Β½(__q__+3) points with a conic π have size at most Β½(__q__+3)+2, with only two exceptions, both due to Pellegrino, which are comp