Solve general quadratic form tuple isometry in characteristic two

Determine whether the quadratic form tuple isometry problem over $\mathbb{F}_2$ can be solved in the general case, without the regularity condition required by the previously known algorithm.

Background

The paper explains that prior algorithms for quadratic form tuple equivalence over F2\mathbb{F}_2 work only under a regularity condition. That restriction prevents them from handling, for example, tuples with an even number of variables. The cited prior work therefore explicitly leaves the unrestricted, general quadratic form tuple isometry problem unresolved; the present paper addresses the general problem through new algorithms and reductions.

References

There is also a different algorithm for quadratic form tuple equivalence in , but that algorithm only works under a regular condition. For example, because of the regular condition, their algorithm does not work with even number of variables. Indeed, an open question in is about the general case of quadratic form tuple isometry.

— Beyond odd characteristic: Faster isomorphism testing of 2-groups of Frattini class 2  (2610.00874 - Grochow et al., 1 Oct 2026) in Section 1, subsection “The significance of 2-groups of Frattini class 2,” footnote following the discussion of the characteristic-two tuple-isometry obstacle