Polynomial multiplicities over finite fields and intersection sets

Bruen, Aiden A.

doi:10.1016/0097-3165(92)90035-s

Cited by 55 publications

(41 citation statements)

References 3 publications

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“…Since F (U, V ) vanishes at least t times for all (u, v) ∈ F 2 q , it can be written as [3,4]. Considering the homogeneous part of largest degree and substituting V = 1, we get…”

Section: Blocking Sets Lacunary Polynomials and Algebraic Curvesmentioning

confidence: 99%

On multiple blocking sets in Galois planes

Blokhuis

Lovász

Storme

et al. 2007

Advg

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This article continues the study of multiple blocking sets in PG(2, q). In [3], using lacunary polynomials, it was proven that t-fold blocking sets of PG(2, q), q square, t < q 1/4 /2, of size smaller than t(q + 1) + c q q 2/3 , with c q = 2 −1/3 when q is a power of 2 or 3 and c q = 1 otherwise, contain the union of t pairwise disjoint Baer subplanes when t ≥ 2, or a line or a Baer subplane when t = 1. We now combine the method of lacunary polynomials with the use of algebraic curves to improve the known characterization results on multiple blocking sets and to prove a t (mod p) result on small t-fold blocking sets of PG(2, q = p n ), p prime, n ≥ 1.

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“…Since F (U, V ) vanishes at least t times for all (u, v) ∈ F 2 q , it can be written as [3,4]. Considering the homogeneous part of largest degree and substituting V = 1, we get…”

Section: Blocking Sets Lacunary Polynomials and Algebraic Curvesmentioning

confidence: 99%

On multiple blocking sets in Galois planes

Blokhuis

Lovász

Storme

et al. 2007

Advg

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“…is contained in C ∩X 4 . Since the former set is a line we have {0123, 0124} ⊆ C. Hence ) and thus C = C .…”

Section: Technical Resultsmentioning

confidence: 99%

5‐chromatic steiner triple systems

Fugere

Haddad

Wehlau

1994

J of Combinatorial Designs

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“…The bound of Bruen [3] |B| ≥ (t + s − 1)(q − 1) + 1, is a general lower bound, which improves on the trivial |B| ≥ tq for t ≤ (s−1)(q −1). This bound had been obtained previously for t = 1 by Jamison [5] and Brouwer and Schrijver [2].…”

Section: Linear Codes Over a Prime Fieldmentioning

confidence: 87%