Hadamard diagonalizable graphs of order at most 36
Jane Breen, Steve Butler, Melissa Fuentes, Bernard Lidický, Michael Philips, Alexander W. N. Riasanovsky, Sung-Yell Song, Ralihe R. Villagrán, Cedar Wiesman, Xiaohong Zhang
This page is containing computer assisted parts of the paper titled
Hadamard diagonalizable graphs of order at most 36.
A preliminary version of the paper can be downloaded here.
You can download the small technical things as one archive
Other (pre)requisites for redoing the entire calculation
Sage Math for running the sage program
C++ compiler on MacOSX or Linux rebuilding the C++ version of the program
nauty for rebuilding the C++ program
Description of the files
Each line contains one Hadamard matrix encoded as a string. For example, the first line is:
Each letter corresponds to 4 entries in the matrix. Highest bit comes first and bit 1 corresponds to 1 in the matrix and 0 to -1 in the matrix.
Notice the string has 256 characters and 256*4 = 1024 = 32 * 32.
Each line contains one graph on 32 vertices. For example line 3 is:
It is in graph6 format, which is easy to load in programs such ase Sage.
Each line corresponds to one matrix.
The first line corresponds to the first line in all_hadamard.txt.
Then the list of numbers correspond to lines in all_of_them_unique.sorted.tx. Example in the file all_indexes.txt the first line is
0 30 53 8498 8506 8897 10021 10161 10191 10195
This means that the first matrix produces Hadamard graphs on lines (0+1), (30+1), (53+1),.... in file all_of_them_unique.sorted.tx.