Class of boolean functions constructed using significant bits of linear recurrences over the ring z2n

In this paper, we study a class of functions built with the help of significant bits sequences on the ring Z₂n. This class is built with the use of a function ф : Z₂n m Z₂. In public literature, there are results for a linear function ф. Here, we use a non-linear ф function for this set. The period of a polynomial F in the ring Z₂n is equal to T(F mod 2)2^a, where a G {0,..., n - 1}. The polynomials for which T(F) = T(F mod 2), i.e. a = 0, are called marked polynomials. For our class, we use a marked polynomial of the maximum period. We show the bounds of the given class: non-linearity, the weight of the functions, the Hamming distance between functions. The Hamming distance between these functions and functions of other known classes is also given.

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