A Novel Approach to Counterexamples of the Polujan-Pott Conjecture via Set-Partition Permutations

In this paper, we settle a conjecture of Polujan and Pott by constructing an explicit, infinite family of Maiorana–McFarland bent functions $f_t$ in $2(2^t-1)$ variables with algebraic degree $\mathrm{°}(f_t)=t+1$ for any integer $t\ge 2$. Our construction builds upon a minimal commutative algebra $I_t$, which naturally induces a triangular set-partition polynomial permutation $P_t$. By identifying an elementary abelian subgroup within the direct sum $I_t\oplus I_t^{\ast }$, we establish an explicit nonlinear coordinate transformation that pulls $f_t$ back to a canonical quadratic form. This linearizes the translation development $\mathrm{Dev}(D_{f_t})$ under an exotic group structure and proves that it is isomorphic to the classical symplectic design $S^{\pm }(2(2^t-1))$, thereby fully resolving the conjecture.