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function algebraic degree

I need to create a general form of ANF of degree d, so I could substitute values of x in it to find the actual ANF of the function. I'm trying to write an algorithm that calculate Algebraic Immunuty of the function of degree d.

1.Substitute all N arguments x with f(x) = 1 in the ANF of a general boolean function g(x) of degree d. This gives a system of N linear equations for the coefficients of g(x). 2. Solve this linear system. 3. If there is no (nontrivial) solution, output no annihilator of degree d, else determine sets of coefficients for linearly independent annihilators.

function algebraic degreeGeneral form of ANF of degree d

I need to create a general form of ANF of degree d, so I ~~could~~ could substitute values of x in it to find the actual ANF of the ~~function.~~ function.

I'm trying to write an algorithm that ~~calculate Algebraic Immunuty~~ calculates algebraic immunity of the function of degree d.

1.Substitute

Substitute all N arguments x with f(x) = 1 in the ~~ANF~~ ANF of a general boolean function g(x) of degree d. d. This gives a system of N linear equations for the coefficients of ~~g(x). 2.~~ g(x).

Solve this linear ~~system. 3.~~ system.

If there is no (nontrivial) solution, output no annihilator of degree d, d, else determine sets of coefficients for linearly independent annihilators.