Some Polynomials Generating Minimal Clones
Hajime Machida and Michael Pinsker
A minimal clone is an atom of the lattice of clones. A minimal function is a function which generates a minimal clone. We consider the base set with k elements for a prime k as a finite field and treat functions as polynomials over GF(k).
Starting from binary minimal functions over GF(3), we generalize some of them and obtain binary minimal functions expressed as polynomials over GF(k) for any prime k ≥ 3.