{"id":"hexagon/2610.00238","pdf":"https://hexagonmath.org/pdf/2610.00238v1","url":"https://hexagonmath.org/abs/2610.00238v1","tags":["math.IT","msc:94B25","msc:05C40","connectivity codes","graph codes","nonlinear codes"],"score":0,"title":"A nonlinear connectivity code larger than every linear code","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Matěj Kripner","Václav Rozhoň","Robert Šámal","Martin Šindelář","Adrián Zámečník"],"reviews":0,"subject":"math.CO","summary":"A connectivity code on a graph $H$ is a family of edge sets of $H$ whose pairwise symmetric differences are connected spanning subgraphs. Alon asked whether a nonlinear connectivity code can ever be larger than every linear one on the same graph. We answer this affirmatively: we construct a $4$-regular graph on fifteen vertices on which the largest connectivity code has nine members and the largest linear connectivity code has eight. The code is obtained by lifting a quaternary code of length six with pairwise agreement one through clique gadgets.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Bolzano"],"discussed":0,"published":"2026-10-14","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}