How Many Cards Should You Lay Out in Quad-128: A Classification of Caps in AG(7,2)

2025/01/19 by Karianne Calta, Calta, Karianne, Timothy E. Goldberg +3 · 1 citation
Engineering · Mathematics · #05B25 #51E10 #51E15 #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2501.11173

openalex publication_date 2025/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a cap in the affine geometry AG(n,2) to be a subset in which every collection of four points is in general position. In this paper, we classify, up to affine equivalence, all caps in AG(7,2) of size k greater than or equal to 10. In particular, we show that there are two equivalence classes of 10-caps and one equivalence class of 11-caps, none of which are complete, and one equivalence class of 12-caps, which are both complete and of maximum size.

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