Weil
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Weight distributions of two classes of linear codes with few weights derived from Weil sums
arXiv:2510.25578v2 Announce Type: replace Abstract: Linear codes with few weights have been a subject of study for many years, as they have applications in secret sharing, authentication codes, association schemes, and strongly regular graphs. In this article, two distinct classes of $p$-ary linear codes are constructed through the selection of two specific defining sets. Their weight distributions are completely determined for each case by detailed calculations on certain Weil sums.
Wadephuls Kampf um Deutschlands Sitz im UN-Sicherheitsrat
Listen on Spotify Apple Music Amazon Music Für die Bundesregierung steht in New York viel auf dem Spiel. Deutschland will wieder einen der begehrten, nichtständigen Sitze im UN-Sicherheitsrat für die Jahre 2027 und 2028. Aber aus der Bewerbung ist ein knallharter Postenpoker geworden: Weil sich neben Deutschland auch Portugal und Österreich bewerben, droht kommende Woche eine Kampfabstimmung.
Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography
Announce Type: replace-cross Abstract: In this work we study quantitative existence results for genus-$2$ curves over $\mathbb{Q}$ whose Jacobians have Mordell--Weil rank at least $1$ or $2$, ordering the curves by the naive height of their integral Weierstrass models. We use geometric techniques to show that asymptotically the Jacobians of almost all integral models with two rational points at infinity have rank $r \geq Since there are $\asymp X^{\frac{13}{2}}$ such models among the $X^7$...
New route to tailor-made diamond nanoparticles holds promise for quantum applications
New route to tailor-made diamond nanoparticles holds promise for quantum applications Stephanie Baum Scientific Editor Robert Egan Associate Editor Nanodiamonds are tiny diamond particles only a few nanometers in size. Because they are chemically highly stable and can host so-called color centers, optically active defects in the crystal lattice, they are considered promising materials for quantum technologies, sensing and biomedical research. Until now, however, it has been difficult to...
River cruise boom: why holidays on the water are trending
River cruises are evolving from a niche product into a key part of Europe's travel market. Rising demand on the German Rhine is increasing pressure on infrastructure. Cruises have long been established in the mainstream travel market.
Exact output statistics of Icart's encoding in the exceptional \(j=0\) case
Announce Type: cross Abstract: Icart's encoding is a classical deterministic map from finite fields to elliptic curves and a basic ingredient in early hash-to-curve constructions. We determine the exact one-output distribution of this map in the exceptional \(j=0\) case. More precisely, for \[ E_{0,b}:Y^2=X^3+b,\ q\equiv2\pmod3, \] we compute the complete fibre distribution of \(f_{0,b}:\mathbb F_q\to E_{0,b}(\mathbb F_q)\).
American Christians Face a Choice
ROBERT JEFFRESS, the pastor of the First Baptist Church in Dallas, has long been one of Donald Trump’s most fawning supporters. By his own account, one reason for his loyalty is that Trump embodies an ethic—cruel, vengeful, and mendacious—that Jeffress and many millions of evangelicals and fundamentalists not only tolerate but welcome. In an NPR interview in 2016, Jeffress explained, “I don’t want some meek and mild leader or somebody who’s going to turn the other cheek.