Upper bounds on the numbers of resilient functions and of bent functions
نویسندگان
چکیده
Bent and resilient functions play significant roles in cryptography, coding theory, and combinatorics. However, the numbers of bent and resilient functions on a given number of variables are not known. Even a reasonable bound on the number of bent functions is not known and the best known bound on the number of resilient functions seems weak for functions of high orders. In this paper we present new bounds which significantly improve upon those which can be directly deduced from the restrictions on the degrees of these functions. In the case of bent functions, it is the first one of this type. In the case of m-resilient functions, it improves upon the known bounds for m large.
منابع مشابه
Coefficient Bounds for Analytic bi-Bazileviv{c} Functions Related to Shell-like Curves Connected with Fibonacci Numbers
In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers. Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.
متن کاملTwo Equivalent Presentations for the Norm of Weighted Spaces of Holomorphic Functions on the Upper Half-plane
Introduction In this paper, we intend to show that without any certain growth condition on the weight function, we always able to present a weighted sup-norm on the upper half plane in terms of weighted sup-norm on the unit disc and supremum of holomorphic functions on the certain lines in the upper half plane. Material and methods We use a certain transform between the unit dick and the uppe...
متن کاملAn interactive weighted fuzzy goal programming technique to solve multi-objective reliability optimization problem
This paper presents an application of interactive fuzzy goal programming to the nonlinear multi-objective reliability optimization problem considering system reliability and cost of the system as objective functions. As the decision maker always have an intention to produce highly reliable system with minimum cost, therefore, we introduce the interactive method to design a high productivity sys...
متن کاملOn Integral Operator and Argument Estimation of a Novel Subclass of Harmonic Univalent Functions
Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...
متن کاملInequalities of Ando's Type for $n$-convex Functions
By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
متن کامل