[图书][B] Extremal finite set theory

D Gerbner, B Patkós - 2018 - taylorfrancis.com
Extremal Finite Set Theory surveys old and new results in the area of extremal set system
theory. It presents an overview of the main techniques and tools (shifting, the cycle method …

Strong blocking sets and minimal codes from expander graphs

N Alon, A Bishnoi, S Das, A Neri - Transactions of the American …, 2024 - ams.org
A strong blocking set in a finite projective space is a set of points that intersects each
hyperplane in a spanning set. We provide a new graph theoretic construction of such sets …

Short minimal codes and covering codes via strong blocking sets in projective spaces

T Héger, ZL Nagy - IEEE Transactions on Information Theory, 2021 - ieeexplore.ieee.org
Minimal linear codes are in one-to-one correspondence with special types of blocking sets
of projective spaces over a finite field, which are called strong or cutting blocking sets …

On cutting blocking sets and their codes

D Bartoli, A Cossidente, G Marino, F Pavese - Forum Mathematicum, 2022 - degruyter.com
Let PG⁡(r, q) be the r-dimensional projective space over the finite field GF⁡(q). A set 𝒳 of
points of PG⁡(r, q) is a cutting blocking set if for each hyperplane Π of PG⁡(r, q) the set Π∩ …

Higgledy-piggledy sets in projective spaces of small dimension

L Denaux - arXiv preprint arXiv:2109.08572, 2021 - arxiv.org
This work focuses on higgledy-piggledy sets of $ k $-subspaces in $\text {PG}(N, q) $, ie sets
of projective subspaces that are'well-spread-out'. More precisely, the set of intersection …

Lines in higgledy-piggledy arrangement

SL Fancsali, P Sziklai - the electronic journal of combinatorics, 2014 - combinatorics.org
In this article, we examine sets of lines in $\mathsf {PG}(d,\mathbb {F}) $ meeting each
hyperplane in a generator set of points. We prove that such a set has to contain at least …

[HTML][HTML] Resolving sets for higher dimensional projective spaces

D Bartoli, G Kiss, S Marcugini, F Pambianco - Finite Fields and Their …, 2020 - Elsevier
Resolving sets for higher dimensional projective spaces - ScienceDirect Skip to main
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Higgledy-piggledy subspaces and uniform subspace designs

SL Fancsali, P Sziklai - Designs, Codes and Cryptography, 2016 - Springer
In this article, we investigate collections of 'well-spread-out'projective (and linear)
subspaces. Projective k-subspaces in PG (d, F) PG (d, F) are in 'higgledy-piggledy …

[HTML][HTML] All minimal [9, 4] 2-codes are hyperbolic quadrics

V Smaldore - Examples and Counterexamples, 2023 - Elsevier
Minimal codes are being intensively studied in last years.[n, k] q-minimal linear codes are in
bijection with strong blocking sets of size n in PG (k− 1, q) and a lower bound for the size of …

[PDF][PDF] Characterising and constructing codes using finite geometries

L Denaux - 2023 - biblio.ugent.be
Characterising and constructing codes using finite geometries Page 1 Characterising and
constructing codes using finite geometries Dissertation submitted in partial fulfilment of the …