Forbidden intersections for codes

Abstract Determining the maximum size of a ‐intersecting code in was longstanding open problem Frankl and Füredi, solved independently by Ahlswede Khachatrian Tokushige. We extend their result to setting forbidden intersections, showing that for any large compared with (but not necessarily ) same bound holds codes weaker property being ‐avoiding, is, having no two vectors agree on exactly coordinates. Our proof proceeds via junta approximation independent interest, which we prove development our recent theory global hypercontractivity: show ‐avoiding is approximately contained (a where membership determined constant number coordinates). In particular, when , this gives an alternative Eberhard, Kahn, Narayanan Spirkl symmetric intersecting have .