2026/07/21 by Christian Lysenstoeen
Computer Science · Mathematics · #cs.IT #math.CO #math.IT
Let A(n,d,w) denote the maximum size of a binary constant-weight code of length n, minimum distance d, and weight w. We construct explicit codes proving A(23,6,10)≥ 2979 and A(24,6,10)≥ 4214. These improve the best surviving explicit codes of sizes 2969 and 4174 and surpass the corresponding 1990 bounds 2970 and 4200 of Brouwer, Shearer, Sloane and Smith, whose code listings were lost. We also obtain A(23,6,11)≥ 3539 and A(24,6,8)≥ 1855. All four bounds are now listed in Brouwer's online table. The constructions use a coordinate decomposition in which one half is fixed to a known code and the complementary half is selected from its full cross-compatible pool using CHILS for maximum-weight independent set. For the 2969-word A(23,6,10) incumbent, exact computations with two solver families prove insertion maximality and exclude every improving exchange deleting at most three codewords. We also analyze codes invariant under prime-order permutations: several cycle types are excluded exactly, the 5+118 type has upper bound 499, and reproducible heuristic saturation evidence is reported for the remaining types, with 13+110 left open. Code files, an independent validator, model descriptions, and computational logs are released.