2019/03/25 by James Aaronson, Aaronson, James, Carla Groenland +3
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1903.10613
openalex publication_date 2019/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subspace of \mathbbF2n is called cyclically covering if every vector in \mathbbF2n has a cyclic shift which is inside the subspace. Let h2(n) denote the largest possible codimension of a cyclically covering subspace of \mathbbF2n. 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.