Cyclically covering subspaces in [formula omitted

Abstract

A subspace of F2n is called cyclically covering if every vector in F2n has a cyclic shift which is inside the subspace. Let h2(n) denote the largest possible codimension of a cyclically covering subspace of F2n. We show that h2(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 h2(ab) depending on h2(a) and h2(b) and extend some of our results to a more general set-up proposed by Cameron, Ellis and Raynaud.