Improved Bounds on Sizes of Generalized Caps in $AG(n,q)$

DOI10.1137/20M1369439zbMath1466.51004arXiv2002.09521MaRDI QIDQ5857007

Publication date: 30 March 2021

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.09521

zbMATH Keywords

combinatorial number theory points in general position capset problem

Mathematics Subject Classification ID

Finite affine and projective planes (geometric aspects) (51E15) Other combinatorial number theory (11B75) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Extremal combinatorics (05D99)

Related Items (2)

A Small Maximal Sidon Set in ${\mathbb{Z}}_2^n$ ⋮ How many cards should you lay out in a game of \textit{EvenQuads}: a detailed study of caps in $\mathrm{AG}(n, 2)$

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Progression-free sets in $\mathbb{Z}_4^n$ are exponentially small
On large subsets of $\mathbb{F}_q^n$ with no three-term arithmetic progression
Differential cryptanalysis of DES-like cryptosystems
On subsets of $\mathbb F_q^n$ containing no $k$-term progressions
Maximal caps in $\mathrm{AG}(6,3)$.
Codes, bent functions and permutations suitable for DES-like cryptosystems
A class of functions and their application in constructing semi-biplanes and association schemes
Extensions of generalized product caps
Uniformly packed codes and more distance regular graphs from crooked functions
On $k$-caps in $\mathrm{PG}(n, q)$, with $q$ even and $n \geq 4$
On $k$-caps in $\mathrm{PG}(n, q)$, with $q$ even and $n \geq 3$
On APN exponents, characterizations of differentially uniform functions by the Walsh transform, and related cyclic-difference-set-like structures
The classification of the largest caps in AG(5, 3)
Codes, graphs, and schemes from nonlinear functions
On subsets of finite Abelian groups with no 3-term arithmetic progressions
Bounds on sizes of generalized caps in $\mathrm{AG} (n,q)$ via the Croot-Lev-Pach polynomial method
Sidon sets and 2-caps in $\mathbb{F}_3^n$
A complete annotated bibliography of work related to Sidon sequences
The number of squares and B_h[g sets]
New bounds on cap sets
A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1.
Perfect nonlinear S-boxes
Solving a linear equation in a set of integers I
Popular progression differences in vector spaces II
An Upper Bound for Weak $B_k$-Sets
New upper bounds for finite $B_h$ sequences
Many $T$ copies in $H$-free graphs

This page was built for publication: Improved Bounds on Sizes of Generalized Caps in $AG(n,q)$