A sufficient and necessary condition of judging the independence of Boolean functions system (Q1906611)

Z. Zhang defined the notion of independence of Boolean functions system. The properties and constructive methods of independent and balanced Boolean functions system are discussed, and its application in cryptology is described. A method judging the independence of balanced Boolean functions system is introduced, which will reduce the independent problem of judging balanced Boolean functions systems to the balanced problem of judging Boolean functions. This is very efficient in some situations. A permutation may be regarded as a special kind of independent and balanced Boolean functions system. Our results may be generalized to residue rings and any finite field, and bring more convenience for the discussion of independence, balance and orthogonality of functions system over residue rings and any finite field.