English

Flat-containing and shift-blocking sets in $F_2^r$

Combinatorics 2013-04-12 v1

Abstract

For non-negative integers rdr\ge d, how small can a subset CF2rC\subset F_2^r be, given that for any vF2rv\in F_2^r there is a dd-flat passing through vv and contained in C{v}C\cup\{v\}? Equivalently, how large can a subset BF2rB\subset F_2^r be, given that for any vF2rv\in F_2^r there is a linear dd-subspace not blocked non-trivially by the translate B+vB+v? A number of lower and upper bounds are obtained.

Cite

@article{arxiv.1304.3233,
  title  = {Flat-containing and shift-blocking sets in $F_2^r$},
  author = {Aart Blokhuis and Vsevolod F. Lev},
  journal= {arXiv preprint arXiv:1304.3233},
  year   = {2013}
}
R2 v1 2026-06-21T23:57:52.053Z