Abstract
AbstractLet $${\mathcal {C}}$$
C
be a 430-cap of $$\textrm{PG}(6,4)$$
PG
(
6
,
4
)
having two intersection sizes with respect to hyperplanes. We show that no hyperplane of $$\textrm{PG}(6,4)$$
PG
(
6
,
4
)
intersects $${\mathcal {C}}$$
C
in a Hill 78-cap. So if it can be shown that the Hill 78-cap of $$\textrm{PG}(5,4)$$
PG
(
5
,
4
)
is projectively unique, then such a 430-cap does not exist, or equivalently, a two-weight $$[430,7]_{\mathbb {F}_4}$$
[
430
,
7
]
F
4
linear code with dual weight at least 4, does not exist.
Funder
University of Western Australia
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications
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