Balanced Symmetric Functions Over GF(p)
نویسندگان
چکیده
Under mild conditions on n, p, we give a lower bound on the number of n-variable balanced symmetric polynomials over finite fields GF (p), where p is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we prove that X(2, 2`− 1) are balanced and conjecture that these are the only balanced symmetric polynomials over GF (2), where X(d, n) = ∑ 1≤i1<i2<···<id≤n xi1xi2 · · ·xid .
منابع مشابه
Enumeration of Balanced Symmetric Functions over GF(p)
It is proved that the construction and enumeration of the number of balanced symmetric functions over GF (p) are equivalent to solving an equation system and enumerating the solutions. Furthermore, we give an lower bound on number of balanced symmetric functions over GF (p), and the lower bound provides best known results.
متن کاملImproved lower bound on the number of balanced symmetric functions over GF
The lower bound on the number of n-variable balanced symmetric functions over finite fields GF(p) presented in [1] is improved in this paper.
متن کاملar X iv : m at h . C O / 0 60 83 69 v 1 1 5 A ug 2 00 6 BALANCED SYMMETRIC FUNCTIONS OVER GF ( p )
Under mild conditions on n, p, we give a lower bound on the number of n-variable balanced symmetric polynomials over finite fields GF (p), where p is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we conjecture that X(2, 2t+1l− 1) are the only nonlinear balanced elementary symmetric polynomials over GF (2), where X...
متن کاملOn a conjecture for balanced symmetric Boolean functions
We give some results towards the conjecture that X(2, 2`− 1) are the only nonlinear balanced elementary symmetric polynomials over GF (2), where t and ` are any positive integers and X(d, n) = ∑ 1≤i1<i2<···<id≤n xi1xi2 · · ·xid .
متن کاملCounting rotation symmetric functions using Polya's theorem
Homogeneous rotation symmetric (invariant under cyclic permutation of the variables) Boolean functions have been extensively studied in recent years due to their applications in cryptography. In this paper we give an explicit formula for the number of homogeneous rotation symmetric functions over the finite field GF(pm) using Polya’s enumeration theorem, which completely solves the open problem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 54 شماره
صفحات -
تاریخ انتشار 2008