Classification of Boolean Cubic Forms in Ten Variables
Number Theory
2026-06-26 v1 Information Theory
Combinatorics
Abstract
We classify Boolean cubic forms in ten variables up to GL(10,2)-equivalence. The catalog contains all 3691560 nonzero orbits. For every orbit we provide a representative with small monomial count, the stabilizer order, and the alternating rank together with an explicit decomposition. The classification is obtained by rank-stratified enumeration. We verify completeness by the Burnside orbit count and independently by the orbit--stabilizer identity. We also provide a fast, complete GL(10,2)-invariant. By polarization, this gives the first complete classification of alternating trilinear forms in dimension 10 over GF(2).
Cite
@article{arxiv.2606.28473,
title = {Classification of Boolean Cubic Forms in Ten Variables},
author = {Kirill Khoruzhii and Patrick Gelß and Sebastian Pokutta},
journal= {arXiv preprint arXiv:2606.28473},
year = {2026}
}