Related papers: Internal and external partial difference families …
Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference…
External difference families (EDFs) are combinatorial objects which were introduced in the early 2000s, motivated by information security applications such as the construction of AMD codes. Various generalizations have since been defined…
Skew partial difference sets (skew PDSs) are recently-introduced combinatorial objects closely related to partial difference sets (PDSs). To date, only one construction approach for non-trivial skew PDSs is known, using bent partitions:…
Classical strong external difference families (SEDFs) are much-studied combinatorial structures motivated by information security applications; it is conjectured that only one classical abelian SEDF exists with more than two sets. Recently,…
(Strong) circular external difference families (which we denote as CEDFs and SCEDFs) can be used to construct nonmalleable threshold schemes. They are a variation of (strong) external difference families, which have been extensively studied…
Circular external difference families (CEDFs) are a recently-introduced variation of external difference families with applications to non-malleable threshold schemes: a $(v,m,\ell,1)$-CEDF is an $m$-sequence $(A_0, \ldots, A_{m-1})$ of…
Strong external difference family (SEDF) and its generalizations GSEDF, BGSEDF in a finite abelian group $G$ are combinatorial designs raised by Paterson and Stinson [7] in 2016 and have applications in communication theory to construct…
Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the…
A $(G,[k_1,\dots,k_t],\lambda)$ {\it partitioned difference family} (PDF) is a partition $\cal B$ of an additive group $G$ into sets ({\it blocks}) of sizes $k_1$, \dots, $k_t$, such that the list of differences of ${\cal B}$ covers exactly…
Strong external difference families (SEDFs) were introduced by Paterson and Stinson as a more restrictive version of external difference families. SEDFs can be used to produce optimal strong algebraic manipulation detection codes. In this…
The circular external difference family and its strong version, which themselves are of independent combinatorial interest, were proposed as variants of the difference family to construct new unconditionally secure non-malleable threshold…
Strong external difference families (SEDFs) have applications to cryptography and are rich combinatorial structures in their own right; until now, all SEDFs have been in abelian groups. In this paper, we consider SEDFs in both abelian and…
We consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external diferences that occur, and were first defined in the context of classifying optimal…
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
Solving partial differential equations (PDEs) on complex domains can present significant computational challenges. The Diffuse Domain Method (DDM) is an alternative that reformulates the partial differential equations on a larger, simpler…
In this paper, we provide a mathematical framework for characterizing AMD codes that are R-optimal. We introduce a new combinatorial object, the reciprocally-weighted external difference family (RWEDF), which corresponds precisely to an…
Double parton distribution functions (dPDFs) represent a tool to explore the 3D partonic structure of the proton. They can be measured in high energy proton-proton and proton nucleus collisions and encode information on how partons inside a…
The comparison of different sets of PDFs structure functions with the description of the whole sets of experimental data of electromagnetic form factors of the proton and neutron is made in the frame work of our model of t-dependence of…
In this talk we present the results of the investigation on the so called double parton distribution functions (dPDFs), accessible quantities in high energy proton-proton and proton nucleus collisions, in double parton scattering processes…
Double parton distribution functions (DPDFs) are used in the QCD description of double parton scattering. The DPDFs evolve with hard scales through QCD evolution equations which obey nontrivial momentum and valence quark number sum rules.…