The class of balanced algebraic threshold functions | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2018. № 40. DOI: 10.17223/20710410/40/1

The paper proposes an approach to the construction of a class of balanced algebraic threshold functions (ATF). The function / of A;-valued logic is called ATF if there are sequences с = (со, ci,..., c_n), b = (bo, b\,..., bk) of integers and the natural modulus m such that f(x\, x₂, · · ·, x_n) = a b_a ^ (со + c\X\ + c₂x₂ + ... + + c_nx_n) mod m < b_a+i for any a e = {0,1,...,k - 1}. The triple (c;b;m) is called the structure of the function /. The central result of the paper is a class of balanced ATF constructed in the following way: if an ATF / has a structure (c, b ,m) = ((c₀,ci,c₂,...,c_ra); (0,p, 2p,..., hp); kp) where Ci = pq and (q,k) = 1, then this function is balanced. Such functions can be used as coordinate functions of substitutions.