| Popis: |
A subspace of F 2 n is called cyclically covering if every vector in 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 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 ( a b ) 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. |
Full Text from ScienceDirect