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1.
In this article a technique for constructing p-ary bent functions from near-bent functions is presented. This technique is then used to obtain both weakly regular and non-weakly regular bent functions. In particular we present the first known infinite class of non-weakly regular bent functions.  相似文献   

2.
In this paper, we generalize the construction of strongly regular graphs in Tan et al. (J. Comb. Theory, Ser. A 117:668–682, 2010) from ternary bent functions to p-ary bent functions, where p is an odd prime. We obtain strongly regular graphs with three types of parameters. Using certain non-quadratic p-ary bent functions, our constructions can give rise to new strongly regular graphs for small parameters.  相似文献   

3.
Jet Jqm denote the set of m-tuples over the integers modulo q and set i=?1, w = ei(q). As an extension of Rothaus' notion of a bent function, a function f, f: JqmJq1 is called bent if all the Fourier coefficients of wf have unit magnitude. An important feature of these functions is that their out-of-phase autocorrelation value is identically zero. The nature of the Fourier coefficients of a bent function is examined and a proof for the non-existence of bent functions over Jqm, m odd, is given for many values of q of the form q = 2 (mod 4). For every possible value of q and m (other than m odd and q = 2 (mod 4)), constructions of bent functions are provided.  相似文献   

4.
We give a construction of 3-class and 4-class association schemes from s-nonlinear and differentially 2 s -uniform functions, and a construction of p-class association schemes from weakly regular p-ary bent functions, where p is an odd prime.  相似文献   

5.
A New Characterization of Semi-bent and Bent Functions on Finite Fields*   总被引:3,自引:0,他引:3  
We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF(2)-linear combination of Gold functions Tr(x2i+1) is semi-bent over GF(2n), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold functions give rise to semi-bent functions over GF(2p) when p belongs to a certain class of primes. Second, we generalize our results to fields GF(pn) where p is an odd prime and n is odd. In that case, we can determine whether a GF(p)-linear combination of Gold functions Tr(xpi+1) is (generalized) semi-bent or bent by a polynomial GCD computation. Similar to the binary case, simple characterizations of these p-ary semi-bent and bent functions are provided. Parts of this paper were presented at the 2002 IEEE International Symposium on Information Theory [10]  相似文献   

6.
The main goal of this article is to extend the concept of q-special functions of complex variable to q-special matrix functions through the study of a q-gamma and a q-beta matrix function. The q-shifted factorial, q-gamma and q-beta matrix functions are defined and some of their properties are investigated.  相似文献   

7.
In his last letter to Hardy, Ramanujan defined 17 functions f(q), (|q|<1), which he called mock theta functions. Each f(q) has infinitely many exponential singularities at roots of unity, and under radial approach to every such singularity, f(q) has an asymptotic approximation consisting of a finite number of terms with closed exponential factors, plus an error term O(1). We give an example of a q-series in Eulerian form having an approximation with an unclosed exponential factor. Complete asymptotic expansions as q→1 of some shifted q-factorials are given in terms of polylogarithms and Bernoulli polynomials. Supported by the Natural Sciences and Engineering Research Council of Canada.  相似文献   

8.
The main result of this paper asserts that if a function f is in the class Bπ,p, 1 <p < ∞; that is, those p-integrable functions whose Fourier transforms are supported in the interval [ - π, π], then f and its derivatives f(j) j = 1, 2, …, can be recovered from its sampling sequence{f(k)} via the cardinal interpolating spline of degree m in the metric ofL q(ℝ)), 1 <p=q < ∞, or 11 <p=q < ⩽ ∞.  相似文献   

9.
10.
Difference systems of sets (DSS) are important for the construction of codes for synchronization. In this paper, a general construction of optimal and perfect difference systems of sets based on q-ary sequences of period n = −1 (mod q) with difference- balanced property is presented, where q is a prime power. This works for all the known q-ary sequences with ideal autocorrelation, and generalizes the earlier construction based on ternary sequences with ideal autocorrelation. In addition, we construct another class of optimal and perfect difference systems of sets, employing decimation of q-ary d-form sequences of period q m −1 with difference-balanced property, which generalizes the previous construction from power functions.  相似文献   

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