Maximal caps in \(\mathrm{AG}(6,3)\).
type: Item
instance of: scholarly article
title: Maximal caps in \(\mathrm{AG}(6,3)\).
zbMATH Open document ID: 1187.51010
author: Aaron Potechin
published in: Designs, Codes and Cryptography
publication date: 2009-03-31T00:00:00Z
review text: One of the main problems in studying caps in geometry is the investigation of their maximal size in finite affine and projective planes. While quite some of these numbers are known for planes and 3-dimensional spaces, only sporadic results are available in higher dimensions, see for example [\textit{R. C. Bose}, Sankhyā 8, 107--166 (1947; Zbl 0038.09601)], [\textit{Y. Edel} and \textit{J. Bierbrauer}, Des. Codes Cryptography 16, No. 2, 151--160 (1999; Zbl 0935.51008)], [\textit{R. Hill}, Discrete Math. 22, 111--137 (1978; Zbl 0391.51005), Ann. Discrete Math. 18, 433--447 (1983; Zbl 0505.51013)] and [\textit{B. Qvist}, Ann. Acad. Sci. Fenn., Ser. A I 134, 27 S. (1952; Zbl 0049.10801)]. In the paper under review the author proves that there are no complete 44-caps in AG(5,3). This result is used in showing that the maximal size of a cap in \(\mathrm{AG}(6,3)\) is 112 and that such caps are uniquely determined up to affine equivalence.
Mathematics Subject Classification ID: 51E22
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 5536707
zbMATH Keywords: finite geometry
zbMATH Keywords: coding theory
zbMATH Keywords: maximal cap
zbMATH Keywords: AG(6,3)
MaRDI profile type: Publication
full work available at URL: s10623-007-9132-z
OpenAlex ID: W2015568452
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DOI: 10.1007/S10623-007-9132-Z
description: scientific article; zbMATH DE number 5536707