New Method for Constructing Complete Cap Sets
Iskandar Karapetyana, Karen Karapetyana
TL;DR
This paper introduces a novel construction method for complete cap sets in affine geometry, achieving a larger set size in AG(15,3) than previous methods by over 4000 points.
Contribution
The paper presents a new construction technique for complete cap sets that surpasses existing methods in size for AG(15,3).
Findings
Constructed a cap set of size 124928 in AG(15,3)
Exceeds previous known cap set sizes by at least 4096 points
Demonstrates improved construction method for finite geometry applications
Abstract
A cap set in projective or affine geometry over a finite field is a set of points no three of which are collinear. In this paper, we propose a new construction for complete cap sets that yields a cap set of size 124928 in the affine geometry AG(15,3). It should be noted that the constructed cap set in AG(15,3) is more powerful and exceeds at least by 4096 points than those that can be obtained from the previously known ones using the product or doubling constructions.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Coding theory and cryptography · Finite Group Theory Research