Author
Aaronson, J
Groenland, C
Johnston, T
Last updated
2021-11-12T01:38:05.7+00:00
Abstract
A subspace of $\mathbb{F}_2^n$ is called cyclically covering if every vector
in $\mathbb{F}_2^n$ has a cyclic shift which is inside the subspace. Let
$h_2(n)$ denote the largest possible codimension of a cyclically covering
subspace of $\mathbb{F}_2^n$. We show that $h_2(p)= 2$ for every prime $p$ such
that 2 is a primitive root modulo $p$, which, assuming Artin's conjecture,
answers a question of Peter Cameron from 1991. We also prove various bounds on
$h_2(ab)$ depending on $h_2(a)$ and $h_2(b)$ and extend some of our results to
a more general set-up proposed by Cameron, Ellis and Raynaud.
Symplectic ID
990666
Download URL
http://arxiv.org/abs/1903.10613v3
Publication type
Journal Article
Publication date
25 March 2019
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