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

Authors :
Calta, Karianne
Goldberg, Timothy E.
Rose, Lauren L.
Publication Year :
2025

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.<br />Comment: 33 pages, 2 figures, 3 tables

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2501.11173
Document Type :
Working Paper