A308361 The largest codimension of a cyclically covering subspace in GF(2)^n.

0, 0, 1, 0, 2, 2, 2, 0, 3, 2, 2, 3, 2, 3, 3, 0, 4, 3, 2, 3

Offset

1,5

Comments

The codimension of the largest subspace V of GF(2)^n with the following property: any vector v in GF(2)^n has a cyclic shift which is contained in V.

Links

Table of n, a(n) for n=1..20.

James Aaronson, Carla Groenland and Tom Johnston, Cyclically covering subspaces in F_2^n, arXiv:1903.10613 [math.CO], 2019.

Peter Cameron, David Ellis and William Raynaud, Smallest cyclically covering subspaces of F_q^n, and lower bounds in Isbell’s conjecture, arXiv:1810.03485 [math.CO], 2018-2019.

Example

a(3) = 1 because the smallest cyclically covering subspace in GF(2)^3, spanned by (1,0,0) and (0,1,1), has codimension 1.
a(4) = 0 because the only cyclically covering subspace of GF(2)^4 is GF(2)^4 itself.

Crossrefs

Sequence in context: A243310 A197727 A176884 * A347317 A342585 A348288

Adjacent sequences: A308358 A308359 A308360 * A308362 A308363 A308364

Keyword

nonn,hard,more

Author

James Aaronson, May 22 2019

Status

approved