Explicit constructions of separating hash families from algebraic curves over finite fields

Let X be a set of order n and Y be a set of order m. An (n,m,{w ₁, w ₂})-separating hash family is a set of N functions from X to Y such that for any with , |X ₁| = w ₁ and |X ₂| = w ₂, there exists an element such that . In this paper, we provide explicit constructions of separating hash families using algebraic curves over finite fields. In particular, applying the Garcia–Stichtenoth curves, we obtain an infinite class of explicitly constructed (n,m,{w ₁,w ₂})–separating hash families with for fixed m, w ₁, and w ₂. Similar results for strong separating hash families are also obtained. As consequences of our main results, we present explicit constructions of infinite classes of frameproof codes, secure frameproof codes and identifiable parent property codes with length where n is the size of the codes. In fact, all the above explicit constructions of hash families and codes provide the best asymptotic behavior achieving the bound , which substantially improve the results in [ 8, 15, 17] give an answer to the fifth open problem presented in [11].     

叠加码的一些新构作

利用集合的并与直积运算建立了新的二元矩阵,从而在已有的叠加码的基础上构作了一些新的叠加码.     

Binary Fingerprinting Codes

Three binary fingerprinting code classes with properties similar to codes with the identifiable parent property are proposed. In order to compare such codes a new combinatorial quality measure is introduced. In the case of two cooperating pirates the measure is derived for the proposed codes, upper and lower bounds are constructed and the results of computer searches for good codes in the sense of the quality measure are presented. Some properties of the quality measure are also derived.AMS classification:94B60, 94B65     

Empirical Likelihood Inference for AR（p） Model

In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared.     

A Construction for Resolvable Designs and Its Generalizations

 In [14], D.K. Ray-Chaudhuri and R.M. Wilson developed a construction for resolvable designs, making use of free difference families in finite fields, to prove the asymptotic existence of resolvable designs with index unity. In this paper, generalizations of this construction are discussed. First, these generalizations, some of which require free difference families over rings in which there are some units such that their differences are still units, are used to construct frames, resolvable designs and resolvable (modified) group divisible designs with index not less than one. Secondly, this construction method is applied to resolvable perfect Mendelsohn designs. Thirdly, cardinalities of such sets of units are investigated. Finally, composition theorems for free difference families via difference matrices are described. They can be utilized to produce some new examples of resolvable designs.