On cutting blocking sets and their codes
Daniele Bartoli, Antonio Cossidente, Giuseppe Marino, Francesco Pavese

TL;DR
This paper introduces new constructions of cutting blocking sets in projective spaces, leading to smaller sets and improved bounds for saturating sets and minimal linear codes, with implications for coding theory.
Contribution
It presents novel constructions of cutting blocking sets in PG(3, q^3) and PG(5, q), reducing their sizes compared to known sets, and improves bounds on saturating sets and minimal code lengths.
Findings
New smaller cutting blocking sets in PG(3, q^3) and PG(5, q)
Linear growth of minimal code length with respect to dimension
Improved upper bounds for saturating sets and minimal code lengths
Abstract
Let PG be the -dimensional projective space over the finite field . A set of points of PG is a cutting blocking set if for each hyperplane of PG the set spans . Cutting blocking sets give rise to saturating sets and minimal linear codes and those having size as small as possible are of particular interest. We observe that from a cutting blocking set obtained by Fancsali and Sziklai, by using a set of pairwise disjoint lines, there arises a minimal linear code whose length grows linearly with respect to its dimension. We also provide two distinct constructions: a cutting blocking set of PG of size as a union of three pairwise disjoint -order subgeometries and a cutting blocking set of PG of size from seven lines of a Desarguesian line spread of PG. In both…
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