English

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

R2 v1 2026-06-23T01:18:29.137Z