共查询到20条相似文献,搜索用时 31 毫秒
1.
Iiro Honkala 《Journal of Algebraic Combinatorics》1992,1(4):347-351
We give a construction of (n–s)-surjective matrices with n columns over
using Abelian groups and additive s-bases. In particular we show that the minimum number of rows ms
q(n,n–s) in such a matrix is at most s
s
q
n–s for all q, n and s. 相似文献
2.
We characterize the finite Veronesean
of all Hermitian varieties of PG(n,q2) as the unique representation of PG(n,q2) in PG(d,q), d n(n+2), where points and lines of PG(n,q2) are represented by points and ovoids of solids, respectively, of PG(d,q), with the only condition that the point set of PG(d,q) corresponding to the point set of PG(n,q2) generates PG(d,q). Using this result for n=2, we show that
is characterized by the following properties: (1)
; (2) each hyperplane of PG(8,q) meets
in q2+1, q3+1 or q3+q2+1 points; (3) each solid of PG(8,q) having at least q+3 points in common with
shares exactly q2+1 points with it.51E24 相似文献
3.
We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p
e) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in
and
. We also give slightly weaker bounds for more general finite classical polar spaces. Another application is the determination of certain explicit bases for the code of PG(2, p) using secants, or tangents and passants, of a nondegenerate conic. 相似文献
4.
Let Ω and
be a subset of Σ = PG(2n−1,q) and a subset of PG(2n,q) respectively, with Σ ⊂ PG(2n,q) and
. Denote by K the cone of vertex Ω and base
and consider the point set B defined by
in the André, Bruck-Bose representation of PG(2,qn) in PG(2n,q) associated to a regular spread
of PG(2n−1,q). We are interested in finding conditions on
and Ω in order to force the set B to be a minimal blocking set in PG(2,qn) . Our interest is motivated by the following observation. Assume a Property α of the pair (Ω,
) forces B to turn out a minimal blocking set. Then one can try to find new classes of minimal blocking sets working with the list of
all known pairs (Ω,
) with Property α. With this in mind, we deal with the problem in the case Ω is a subspace of PG(2n−1,q) and
a blocking set in a subspace of PG(2n,q); both in a mutually suitable position. We achieve, in this way, new classes and new sizes of minimal blocking sets in PG(2,qn), generalizing the main constructions of [14]. For example, for q = 3h, we get large blocking sets of size qn + 2 + 1 (n≥ 5) and of size greater than qn+2 + qn−6 (n≥ 6). As an application, a characterization of Buekenhout-Metz unitals in PG(2,q2k) is also given. 相似文献
5.
Giuseppe Pellegrino 《Rendiconti del Circolo Matematico di Palermo》1998,47(1):141-168
1. | Letm be the greatest integer such that . ThenPG(3,q) contains complete caps of sizek=(m+1)(q+1)+ω, with ω=0, 1, 2. | |
2. |
PG(3,q),q≥5, contains complete caps of size |
|
3. | InPG(3,q) complete caps different from ovaloids have some external planes. |
6.
Let q 2 be an integer. Then –q gives rise to a number system in
, i.e., each number n
has a unique representation of the form n = c
0 + c
1 (–q) + ... + c
h
(–q)
h
, with c
i
{0,..., q – 1}(0 i h). The aim of this paper is to investigate the sum of digits function –q
(n) of these number systems. In particular, we derive an asymptotic expansion for
and obtain a Gaussian asymptotic distribution result for –q
(n) – –q
(–n). Furthermore, we prove non-differentiability of certain continuous functions occurring in this context. We use automata and analytic methods to derive our results. 相似文献
7.
A t-cover of a quadric
is a set C of t-dimensional subspaces contained in
such that every point of
is contained in at least one element of C.We consider (n – 1)-covers of the hyperbolic quadric Q
+(2n + 1, q). We show that such a cover must have at least q
n + 1 + 2q + 1 elements, give an example of this size for even q and describe what covers of this size should look like. 相似文献
8.
We prove that a GF(q)-linear Rédei blocking set of size q
t + q
t–1 + ··· + q + 1 of PG(2,q
t) defines a derivable partial spread of PG(2t – 1, q). Using such a relationship, we are able to prove that there are at least two inequivalent Rédei minimal blocking sets of size q
t + q
t–1 + ··· + q + 1 in PG(2,q
t), if t 4. 相似文献
9.
The structure of
n– 1-sets inPG(n, q) with more thanq – 1 nuclei is investigated. It is shown that classification of these sets with the maximal numberq
n– 1-q
n– 2 of nuclei is equivalent to the classification of (q + l)-sets inPG(2,q) havingq –1 nuclei.Dedicated to Professer Walter Benz for his 60th birthday 相似文献
10.
Satoshi Yoshiara 《Journal of Algebraic Combinatorics》2004,19(1):5-23
A d-dimensional dual arc in PG(n, q) is a higher dimensional analogue of a dual arc in a projective plane. For every prime power q other than 2, the existence of a d-dimensional dual arc (d 2) in PG(n, q) of a certain size implies n d(d + 3)/2 (Theorem 1). This is best possible, because of the recent construction of d-dimensional dual arcs in PG(d(d + 3)/2, q) of size
d–1
i=0
q
i, using the Veronesean, observed first by Thas and van Maldeghem (Proposition 7). Another construction using caps is given as well (Proposition 10). 相似文献
11.
We show that a maximal partial spread inPG(3,q) is either a spread or has at most
lines. This implies that it is not possible to cover all points but the points of a Baer-subspace by lines. 相似文献
12.
Martin Bokler 《Designs, Codes and Cryptography》2001,24(2):131-144
In this paper minimal m-blocking sets of cardinality at most
in projective spaces PG(n,q) of square order q, q 16, are characterized to be (t, 2(m-t-1))-cones for some t with
. In particular we will find the smallest m-blocking sets that generate the whole space PG(n,q) for 2m n m. 相似文献
13.
Carla Dionisi 《Annali di Matematica Pura ed Applicata》1998,175(1):285-293
Let
be the moduli space of stable symplectic instanton bundles on 2n+1 with second Chern class c2=k (it is a closed subscheme of the moduli space
).We prove that the dimension of its Zariski tangent space at a special (symplectic) instanton bundle is 2k(5n–1)+4n2–10n+3, k2. 相似文献
14.
Tatsuya Maruta 《Geometriae Dedicata》1996,60(1):1-7
A lower bound on the size of a set K in PG(3, q) satisfying
for any plane of PG(3, q), q4 is given. It induces the non-existence of linear [n,4,n + 1 – q
2]-codes over GF(q) attaining the Griesmer bound for
. 相似文献
15.
B. A. Pogorelov 《Mathematical Notes》1974,16(1):640-645
Let PL(n, q) be a complete projective group of semilinear transformations of the projective space P(n–1, q) of projective degree n–l over a finite field of q elements; we consider the group in its natural 2-transitive representation as a subgroup of the symmetric group S(P*(n–1, q)) on the setp*(n–1),q=p(n–1,q)/{O}. In the present note we show that for arbitrary n satisfying the inequality n>4[(qn–1)/(qn–1–1)] [in particular, for n>4(q +l)] and for an arbitrary substitutiong s (p*(n–1,q))pL(n,q) the group PL(n,q), g contains the alternating group A(P* (n–1,q)). Forq=2, 3 this result is extended to all n3.Translated from Matematicheskie Zametki, Vol. 16, No. 1, pp. 91–100, July, 1974.The author expresses his sincere thanks to M. M. Glukhov for his interest in his work. 相似文献
16.
Laurel L. Carpenter 《Designs, Codes and Cryptography》1996,9(1):51-59
Given any protective plane of even order q containing a hyperoval
, a Steiner
design can be constructed. The 2-rank of this design is bounded above by rank2() – q – 1. Using a result of Blokhuis and Moorhouse [3], we show that this bound is met when is desarguesian and
is regular. We also show that the block graph of the Steiner 2-design in this case produces a Hadamard design which is such that the binary code of the associated 3-design contains a copy of the first-order Reed-Muller code of length 22m
, where q = 2
m
. 相似文献
17.
LetA be a nonsingularn byn matrix over the finite fieldGF
q
,k=n/2,q=p
a
,a1, wherep is prime. LetP(A,q) denote the number of vectorsx in (GF
q
)
n
such that bothx andAx have no zero component. We prove that forn2, and
,P(A,q)[(q–1)(q–3)]
k
(q–2)
n–2k
and describe all matricesA for which the equality holds. We also prove that the result conjectured in [1], namely thatP(A,q)1, is true for allqn+23 orqn+14. 相似文献
18.
The maximum number m
2(n, q) of points in PG(n, q), n2, such that no three are collinear is known precisely for (n, q)=(n,2), (2,q), (3,q), (4, 3), (5,3). In this paper an improved upper bound of order q
n–1
–1/2q
n–2 is obtained for q even when n4 and q>2. A necessary preliminary is an improved upper bound for m2(3, q), the maximum size of a k-cap not contained in an ovoid. It is shown that
and that m2(3, 4)=14. 相似文献
19.
This article first of all discusses the problem of the cardinality of maximal partial spreads in PG(3,q), q square, q>4. Let r be an integer such that 2rq+1 and such that every blocking set of PG(2,q) with at most q+r points contains a Baer subplane. If S is a maximal partial spread of PG(3,q) with q
2-1-r lines, then r=s(
+1) for an integer s2 and the set of points of PG(3,q) not covered byS is the disjoint union of s Baer subgeometriesPG(3,
). We also discuss maximal partial spreads in PG(3,p
3), p=p
0
h
, p
0 prime, p
0 5, h 1, p 5. We show that if p is non-square, then the minimal possible deficiency of such a spread is equal to p
2+p+1, and that if such a maximal partial spread exists, then the set of points of PG(3,p
3) not covered by the lines of the spread is a projected subgeometryPG(5,p) in PG(3,p
3). In PG(3,p
3),p square, for maximal partial spreads of deficiency p
2+p+1, the combined results from the preceding two cases occur. In the final section, we discuss t-spreads in PG(2t+1,q), q square or q a non-square cube power. In the former case, we show that for small deficiencies , the set of holes is a disjoint union of subgeometries PG(2t+1,
), which implies that 0 (mod
+1) and, when (2t+1)(
-1) <q-1, that 2(
+1). In the latter case, the set of holes is the disjoint union of projected subgeometries PG(3t+2,
) and this implies 0 (mod q
2/3+q
1/3+1). A more general result is also presented. 相似文献
20.
Mieko Yamada 《Combinatorica》1988,8(2):207-216
Letq 3 (mod 4) be a prime power and put
. We consider a cyclic relative difference set with parametersq
2–1,q, 1,q–1 associated with the quadratic extension GF(q2)/GF((q). The even part and the odd part of the cyclic relative difference set taken modulon are
supplementary difference sets. Moreover it turns out that their complementary subsets are identical with the Szekeres difference sets. This result clarifies the true nature of the Szekeres difference sets. We prove these results by using the theory of the relative Gauss sums. 相似文献