Classify ternary maximal self-orthogonal codes of lengths at least 25

Classify ternary maximal self-orthogonal codes of every length $n geq25$ relevant to the construction and enumeration of weighing matrices of weight 9.

Background

The paper’s code-based search for mutually unbiased weighing matrices depends on classifications of ternary maximal self-orthogonal codes. Such classifications are cited for lengths 19 and 21–23, and ternary self-dual codes are classified at length 24. Beyond length 24, the absence of a classification prevents the authors from extending their systematic search, and they stop investigating orders above 24.

References

For $n \geq 25$, a classification of ternary maximal self-orthogonal codes of length $n$ has not yet been done. We stopped searching for mutually unbiased weighing matrices of weight $9$ at order $24$.

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