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Williamson sequences

The following files contain an enumeration of all inequivalent Williamson sequences of a given order n which is divisible by 2 or 3 under the following equivalence operations:

  1. Reorder the sequences ABCD in any way.
  2. Negate all the entries in any of ABC, or D.
  3. If n is even, cyclically shift all the entries in any of ABC, or D by an offset of n/2.
  4. Apply an automorphism of the cyclic group Cn to all the indices of the entries of ABC, and D simultaneously.
  5. If n is even, negate every second entry in each of ABC, and D simultaneously.

Every line in each file contains exactly one Williamson sequence, with spaces separating the members ABC and D of the Williamson sequence. The sequence entries are encoded using the characters + for 1 and - for −1. The sequences were constructed using a SAT+CAS method which is described in the paper Applying Computer Algebra Systems with SAT Solvers to the Williamson Conjecture by BrightKotsireas, and Ganesh.  They have also been archived on Zenodo.

order n # sequences filesize
2 1 12
3 1 16
4 1 20
6 1 28
8 1 36
9 3 120
10 2 88
12 3 156
14 5 300
15 4 256
16 6 408
18 23 1.8K
20 17 1.4K
21 7 616
22 15 1.4K
24 72 7.1K
26 26 2.8K
27 6 672
28 83 9.5K
30 150 19K
32 152 20K
33 5 680
34 91 13K
36 477 69K
38 50 7.7K
39 1 160
40 1499 241K
42 301 51K
44 249 44K
45 1 184
46 50 9.2K
48 9800 1.9M
50 275 55K
51 2 416
52 926 192K
54 498 107K
56 40315 8.8M
57 1 232
58 73 17K
60 4083 973K
62 61 16K
63 2 512
64 69960 18M
66 262 69K
68 1113 300K
69 1 280
70 98 28K