Almost homomorphisms between the Boolean cube and groups of prime order
Combinatorics
2018-11-05 v2
Abstract
We show that if f is an injection from an n-dimensional Boolean cube (considered as an additive group) to a group of prime order then the probability that f(x+y)=f(x)+f(y) is O(2^{-n/11}).
Cite
@article{arxiv.1804.03192,
title = {Almost homomorphisms between the Boolean cube and groups of prime order},
author = {Tom Sanders},
journal= {arXiv preprint arXiv:1804.03192},
year = {2018}
}
Comments
7 pages, added an example to section 2, corrected some errors