相关论文: Generalized perfect difference families and their …

Near maximum distance separable (NMDS) codes, where both the code and its dual are almost maximum distance separable, play pivotal roles in combinatorial design theory and cryptographic applications. Despite progress in fixed dimensions…

Roughly speaking, an $(n,(r,s))$-Cover Free Family (CFF) is a small set of $n$-bit strings such that: "in any $d:=r+s$ indices we see all patterns of weight $r$". CFFs have been of interest for a long time both in discrete mathematics as…

We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology at LO and NNLO in perturbative QCD, thereby generalizing to these orders the NNPDF2.1 NLO parton…

We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general $ n $-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The…

We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalisation of the much-studied structures of disjoint difference family (DDF), external difference…

The {\em Fibonacci cube} of dimension $n$, denoted as $\Gamma\_n$, is the subgraph of the $n$-cube $Q\_n$ induced by vertices with no consecutive 1's. In an article of 2016 Ashrafi and his co-authors proved the non-existence of perfect…

In global PDF analyses, parton distribution functions (PDFs) are parametrised at a fixed input scale $Q_0$ and evolved to higher scales using the DGLAP equations. Since QCD evolution is fully determined within perturbation theory, the…

Strong difference families of special types are introduced to produce new relative difference families from the point of view of both asymptotic existences and concrete examples. As applications, group divisible designs of type $30^u$ with…

Motivated by a problem in computer architecture we introduce a notion of the perfect distance-dominating set, PDDS, in a graph. PDDSs constitute a generalization of perfect Lee codes, diameter perfect codes, as well as other codes and…

Constraint Programming (CP) has been successfully applied to both constraint satisfaction and constraint optimization problems. A wide variety of specialized global constraints provide critical assistance in achieving a good model that can…

We propose a unified theory of generalized weights for linear codes endowed with an arbitrary distance. Instead of relying on supports or anticodes, the weights of a code are defined via the intersections of the code with a chosen family of…

Machine learning models with inputs in a Euclidean space $\mathbb{R}^d$, when implemented on digital computers, generalize, and their generalization gap converges to $0$ at a rate of $c/N^{1/2}$ concerning the sample size $N$. However, the…

Let $q=p^m$ be a prime power, $e$ be an integer with $0\leq e\leq m-1$ and $s=\gcd(e,m)$. In this paper, for a vector $v$ and a $q$-ary linear code $C$, we give some necessary and sufficient conditions for the equivalent code $vC$ of $C$…

We study $1$-perfect codes in Doob graphs $D(m,n)$. We show that such codes that are linear over $GR(4^2)$ exist if and only if $n=(4^{g+d}-1)/3$ and $m=(4^{g+2d}-4^{g+d})/6$ for some integers $g \ge 0$ and $d>0$. We also prove necessary…

We study the generic properties of finitely presented monoids and semigroups. We show that for positive integers a > 1, k and m, the generic a-generator k-relation monoid and semigroup presentation (defined in any of several definite…

In this paper, we propose a family of nonconforming finite elements for $2m$-th order partial differential equations in $\mathbb{R}^n$ on simplicial grids when $m=n+1$. This family of nonconforming elements naturally extends the elements…

In 2008, Wang \& Wang showed that the set of gaps of a numerical semigroup generated by two coprime positive integers $a$ and $b$ is equidistributed modulo 2 precisely when $a$ and $b$ are both odd. Shor generalized this in 2022, showing…

In a graph, a perfect matching cut is an edge cut that is a perfect matching. Perfect Matching Cut (PMC) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and…

The existence of quantum error correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum information theory. However, standard error correction refers to abstract quantum…

We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…