It is shown, through an exhaustive search, that there are no circulant symmetric Williamson matrices of order \(39\). The construction of symmetric but not circulant Williamson-type matrices of order \(39\), first given by Miyamoto, Seberry and Yamada, is given explicitly.
Citation
Christos Koukouvinos, Stratis Kounias. There are no Circulant Symmetric Williamson Matrices of Order \(39\)[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 007. 161-169. .