Classification of Cubic Boolean Functions in 7 Variables
نویسندگان
چکیده
A well-known and widely used approach in the study of algebraic objects is the investigation of their sub-objects and quotient objects. Consider the set of Boolean functions on F2 of degree less than or equal to r for 0 ≤ r ≤ n, which can also be seen as the Reed-Muller code RM(r, n) of order r. The automorphism group of RM(r, n) is equal to the general affine group AGL(n, 2) for all 1 ≤ r ≤ n [MS91, Theorem 24]. For −1 ≤ s < r ≤ n, the quotient space of RM(r, n) by the sub-code RM(s, n) is denoted by RM(r, n)/RM(s, n). Consequently, two Boolean functions f1, f2 of RM(r, n)/RM(s, n) are said to be equivalent over RM(s, n) if f1(x) = f2(xA⊕ b)mod RM(s, n). If s = 1, this means that
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