Abstract Let 1 1 be the all-one vector and ⊙ denote the component-wise multiplication of two vectors in F₂ⁿ F 2 n. We study the vector space ₙ Γ n over F₂ F 2 generated by the functions ₂₊: F₂ⁿ F₂ⁿ, k 0 γ 2 k: F 2 n → F 2 n, k ≥ 0, where ₂₊ (x) = S^2k (x) (1+S^2k-1 (x) ) (1+S^2k-3 (x) ) (1+S (x) ) γ 2 k (x) = S 2 k (x) ⊙ (1 + S 2 k - 1 (x) ) ⊙ (1 + S 2 k - 3 (x) ) ⊙ ⋯ ⊙ (1 + S (x) ) and S: F₂ⁿ F₂ⁿ S: F 2 n → F 2 n is the cyclic left shift function. The functions in
Kriepke et al. (2026) studied this question.