On the 430-cap of PG (6 , 4) having two intersection sizes with respect to hyperplanes

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Abstract

Let C be a 430-cap of PG (6 , 4) having two intersection sizes with respect to hyperplanes. We show that no hyperplane of PG (6 , 4) intersects C in a Hill 78-cap. So if it can be shown that the Hill 78-cap of PG (5 , 4) is projectively unique, then such a 430-cap does not exist, or equivalently, a two-weight [430,7]F4 linear code with dual weight at least 4, does not exist.

Original languageEnglish
Pages (from-to)495-503
Number of pages9
JournalDesigns, Codes, and Cryptography
Volume92
Issue number2
Early online date18 Nov 2023
DOIs
Publication statusPublished - Feb 2024

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