Characterization of exotic stabilizer generators

Characterize when exotic generators occur in the F2-stabilizer of the true-Hadamard set for the half-flip family and identify the algebraic invariant of L that determines their number.

Background

For the tested YES lengths L∈{11,19,27,51,59}, the paper records different numbers of exotic generators in the stabilizer beyond five standard generators.

The observed counts are not predicted by L modulo 16 or by primality, so the structural parameter controlling their appearance remains unidentified.

References

A characterization of when exotic generators appear, and what algebraic invariant of $L$ controls their count, remains open.

— An explicit half-flip family of 32-modular Hadamard matrices at L = 3 mod 8: structural placement and mod-tower analysis  (2609.25543 - Kulhandjian, 22 Sep 2026) in Section 6, Open questions