Linear blocking sets in PG(2, q4)
نویسندگان
چکیده
In this paper, by using the geometric construction of linear blocking sets as projections of canonical subgeometries, we determine all the GF (q)linear blocking sets of the plane PG(2, q).
منابع مشابه
Linear Point Sets and Rédei Type k-blocking Sets in PG(n, q)
In this paper, k-blocking sets in PG(n, q), being of Rédei type, are investigated. A standard method to construct Rédei type k-blocking sets in PG(n, q) is to construct a cone having as base a Rédei type k′-blocking set in a subspace of PG(n, q). But also other Rédei type k-blocking sets in PG(n, q), which are not cones, exist. We give in this article a condition on the parameters of a Rédei ty...
متن کاملBlocking Sets and Derivable Partial Spreads
We prove that a GF(q)-linear Rédei blocking set of size qt + qt−1 + · · · + q + 1 of PG(2, qt ) 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 qt + qt−1 + · · · + q + 1 in PG(2, qt ), if t ≥ 4.
متن کاملOn the Linearity of Higher-Dimensional Blocking Sets
A small minimal k-blocking set B in PG(n, q), q = pt, p prime, is a set of less than 3(qk + 1)/2 points in PG(n, q), such that every (n − k)-dimensional space contains at least one point of B and such that no proper subset of B satisfies this property. The linearity conjecture states that all small minimal k-blocking sets in PG(n, q) are linear over a subfield Fpe of Fq. Apart from a few cases,...
متن کاملA proof of the linearity conjecture for k-blocking sets in PG(n, p), p prime
In this paper, we show that a small minimal k-blocking set in PG(n, q), q = p, h ≥ 1, p prime, p ≥ 7, intersecting every (n−k)-space in 1 (mod q) points, is linear. As a corollary, this result shows that all small minimal k-blocking sets in PG(n, p), p prime, p ≥ 7, are Fp-linear, proving the linearity conjecture (see [7]) in the case PG(n, p), p prime, p ≥ 7.
متن کاملOn small blocking sets and their linearity
We prove that a small blocking set of PG(2, q) is “very close” to be a linear blocking set over some subfield GF(p) < GF(q). This implies that (i) a similar result holds in PG(n, q) for small blocking sets with respect to k-dimensional subspaces (0 ≤ k ≤ n) and (ii) most of the intervals in the interval-theorems of Szőnyi and Szőnyi-Weiner are empty.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 26 شماره
صفحات -
تاریخ انتشار 2002