T k denotes the number of inequivalent k-phase sequences of the indicated length L. The term “redundant count” means, for example, that 2-phase, 3-phase, 4-phase, and 6-phase sequences are all… (More)

This paper shows that there is a connection between the crosscorrelation functions of certain binary m-sequences and the value sets of the polynomials xk(1+x)2 m−1 for k ∈ {±1,±2, 4}, where x is in… (More)

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… (More)

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) = ∑… (More)

In this paper we present asymptotic expressions for the number of functions satisfying the Strict Avalanche Criterion (SAC) with respect to one and two variables, previously developed by O’Connor.… (More)

We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu [6]. We give exact results for the nonlinearity and weight of 2-degree RotS functions… (More)

Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such… (More)