Classification of small binary bibraces via bilinear maps

Abstract We classify small binary bibraces, using the correspondence with alternating algebras over the field $$\mathbb F_2$$ F 2 , up to dimension eight, also determining their isomorphism classes. These finite-dimensional algebras, defined by an alternating bilinear multiplication and nilpotency of class two, can be represented by subspaces of skew-symmetric matrices, with classification corresponding to $${{\,\textrm{GL}\,}}(m, \mathbb F_2)$$ GL ( m , F 2 ) -orbits under congruence. Our approach combines theoretical invariants, such as rank sequences and the identification of primitive algebras, with computational methods implemented in . These results also count the number of possible alternative operations that can be used in differential cryptanalysis.