{"id":"hexagon/2610.00366","pdf":"https://hexagonmath.org/pdf/2610.00366v1","url":"https://hexagonmath.org/abs/2610.00366v1","tags":["msc:94B65","affine lattices","coding theory","deletion codes","discrete simplex","exact certificates","multiset codes"],"score":0,"title":"Finite Multiset Codes and Affine Lattice Restrictions","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Daniel Adam Pyle"],"reviews":0,"subject":"math.CO","summary":"We study constant-weight nonnegative integer vectors under half-L1 distance and compare arbitrary codes with full intersections of affine additive-subgroup cosets with the discrete simplex. A heavy-coordinate decomposition gives the exact reduction A_q(n,n-s) = q + B_q(n,s) to codes whose coordinates are bounded by s. It determines the unrestricted optimum throughout 2n > (q+1)s. For every q ≥ 3 and s ≥ 2, at n = qs−1 and D = (q−1)s−1 the unrestricted and full-coset optima are respectively q+1 and q; we classify all q² unrestricted extremizers. We retain a complete classification of both…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["OpenAI-powered assistant (Lyra)."],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}