Circulant Weighing Matrices

Circulant Weighing Matrices

A New Branch of The La Jolla Combinatorial Data Repository


A data repository formerly made available via an SQL server is repackaged as a Jupyter book, with code and data freely available.


Daniel M. Gordon {}

IDA Center for Communications Research 4320 Westerra Court San Diego, CA 92121 USA


A weighing matrix \(W = (w_{i,j})\) is a square matrix of order \(n\) and entries \(w_{i,j}\) in \(\{0, \pm 1\}\) such that \(WW^T=kI_n\). In his thesis, Strassler gave a table of existence results for circulant weighing matrices with \(n \leq 200\) and \(k \leq 100\). Since then, numerous papers have dealt with open cases in the table.

The author recently wrote a paper with K.T. Arasu and Yiran Zhang, resolving 12 more cases. Rather than publishing a new version of the table in that paper, the results were added to the La Jolla Combinatorics Repository, an online database containing results on covering designs, difference sets and Steiner systems. Here we give that data in the form of a Jupyter book, in the hopes of being more compatible with FAIR data management principles.


  title     = {Circulant Weighing Matrices,
  author    = {Gordon Daniel M.},
  year      = {2022},
  doi       = {10.5072/zenodo.1055443}


See also

The author’s website, at, has data repositories for difference sets, covering designs, circulant weighing matrices and Steiner systems.