The following files contain an enumeration the complex Golay pairs of a given length \(n\). The sequences are encoded using the characters + for 1, - for −1, i for \(i\), and j for \(-i\).
The the second column of the table counts how many distinct sequences occur in the complex Golay pairs of length \(n\), the third column counts the total number of complex Golay pairs of length \(n\), and the last column counts the number of inequivalent complex Golay pairs of length \(n\). The equivalence operations are given in the paper Enumeration of Complex Golay Pairs via Programmatic SAT by Bright, Kotsireas, Heinle, and Ganesh. The pairs have also been archived on Zenodo.
length \(n\) | # total seqns | # total pairs | # inequiv pairs |
1 | 4 | 16 | 1 |
2 | 16 | 64 | 1 |
3 | 16 | 128 | 1 |
4 | 64 | 512 | 2 |
5 | 64 | 512 | 1 |
6 | 256 | 2048 | 3 |
7 | 0 | 0 | 0 |
8 | 768 | 6656 | 17 |
9 | 0 | 0 | 0 |
10 | 1536 | 12288 | 20 |
11 | 64 | 512 | 1 |
12 | 4608 | 36864 | 52 |
13 | 64 | 512 | 1 |
14 | 0 | 0 | 0 |
15 | 0 | 0 | 0 |
16 | 13312 | 106496 | 204 |
17 | 0 | 0 | 0 |
18 | 3072 | 24576 | 24 |
19 | 0 | 0 | 0 |
20 | 26880 | 215040 | 340 |
21 | 0 | 0 | 0 |
22 | 1024 | 8192 | 12 |
23 | 0 | 0 | 0 |
24 | 98304 | 786432 | 1056 |
25 | 0 | 0 | 0 |
26 | 1280 | 10240 | 16 |
27 | 0 | 0 | 0 |
28 | 0 | 0 | 0 |