Classify weighing matrices of orders 21–24 and weight 9

Classify all weighing matrices of orders 21, 22, 23, and 24 with weight 9 up to equivalence.

Background

For orders 21 through 24, the paper constructs selected weighing matrices of weight 9 from classified ternary self-orthogonal or self-dual codes and uses them to obtain lower bounds for the maximum sizes of mutually unbiased families. However, the full classifications of weighing matrices themselves have not been completed, so the reported lower and upper bounds for the maximum family sizes are not exact in these orders.

References

For $n=21,22,23,24$, a classification of weighing matrices of order $n$ and weight $9$ has not yet been done.

— Unbiased weighing matrices of weight $9$  (2501.15444 - Araya et al., 26 Jan 2025) in Section 5, subsection “Orders 21, 22, 23, 24”