Small complete caps in PG(r,q), r ⩾ 3
نویسندگان
چکیده
منابع مشابه
Small complete caps in PG(r, q), r >= 3
A very difficult problem for complete caps in PG(r,q) is to determine their minimum size. The results on this topic are still scarce and in this paper we survey the best results now known. Furthermore, we construct new interesting sporadic examples of complete caps in PG(3, q) and in PG(4, q) such that their size are smaller than the currently known. As a consequence, we get that the Pellegrino...
متن کاملSmall complete caps in Galois affine spaces
Some new families of caps in Galois affine spaces AG(N , q) of dimension N ≡ 0 (mod 4) and odd order q are constructed. Such caps are proven to be complete by using some new ideas depending on the concept of a regular point with respect to a complete plane arc. As a corollary, an improvement on the currently known upper bounds on the size of the smallest complete caps in AG(N , q) is obtained.
متن کاملA family of small complete caps in PG(n, 2)
The smallest known complete caps in PG(n, 2) have size 23(2(n−6)/2) − 3 if n ≥ 10 is even and size 15(2(n−5)/2) − 3 if n ≥ 9 is odd. Here we give a simple construction of complete caps in PG(n, 2) of size 24(2(n−6)/2)− 3 if n is even and size 16(2(n−5)/2)− 3 if n is odd. Thus these caps are only slightly larger than the smallest complete caps known in PG(n, 2). © 2003 Elsevier Ltd. All rights r...
متن کاملConstructions of Small Complete Caps in Binary Projective Spaces
In the binary projective spaces PG(n,2) k-caps are called large if k > 2n−1 and small if k ≤ 2n−1. In this paper we propose new constructions producing infinite families of small binary complete caps.
متن کاملLarge Caps in Small Spaces
We construct large caps in projective spaces of small dimension (up to 11) defined over fields of order at most 9. The constructions are both theoretical and computer-supported. Some more computergenerated 4-dimensional caps over larger fields are also mentioned.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00324-x