A binary constant-weight code with A(38,8,5) ≥ 66: first improvement of the best-known lower bound (65 → 66) since 2006

This dataset contains an explicit binary constant-weight code with parametersn = 38 (length), d = 8 (minimum Hamming distance), w = 5 (constant weight),and size M = 66 codewords. Each codeword is a length-38 binary string of weight 5, and any two codewordsare at Hamming distance at least 8 (equivalently, any two codeword supportsshare at most one common position). Significance:This improves the best-known lower bound on A(38,8,5) — the maximum size ofsuch a code — from 65 to 66. The previous value of 65 had been the best knownsince the standard tables for lengths n > 28 (D. H. Smith, L. A. Hughes andS. Perkins, "A New Table of Constant Weight Codes of Length Greater than 28",Electron. J. Combin. 13 (2006), #A2; with improvements by R. Montemanni andD. H. Smith, IEEE Trans. Inf. Theory 55 (2009) 4651–4656). Moreover, 65 wasmerely the trivial value inherited from A(37,8,5) = 65 by adding a zerocoordinate. The code presented here is the first to establishA(38,8,5) > A(37,8,5), i.e., that the 38th coordinate yields a strictimprovement. Since the Johnson bound gives A(38,8,5) ≤ floor((38/5)·floor(37/4)) = 68,the best-known range becomes 66 ≤ A(38,8,5) ≤ 68. File format:Plain text. The first line is a comment header (n, w, d, size). Each subsequentline is one length-38 binary codeword of weight 5. Verification:The code can be verified directly: 66 distinct weight-5 binary words of length 38,with every pair of codewords sharing at most one 1-position (minimum Hammingdistance 8). Author: Ankan SadhuDate: 2026-07-21