7 papers
Counterexamples to Charpin's Conjecture on BCH codes
Run Zheng, Yaoran Yang, Yutong Zhang +2
We construct an infinite family of -ary primitive narrow-sense BCH codes whose minimum distance strictly exceeds the Bose distance; in fact, the gap between the two can be arbit…
The 196560 auxiliary-function conjecture for the Leech lattice
Yutong Zhang, Yaoran Yang
Cohn and Kumar conjectured in 2009 that there is a radial Schwartz function satisfying for , for , $g(2)…
Frobenius-orbit slicing and uniform elimination of positive-dimensional singular loci
Yutong Zhang, Yaoran Yang
Let $\cX\subseteq\Pj^n_{\Z}$ be a fixed integral quasiprojective subscheme, smooth over of relative dimension . For each fixed , we bound the probability that the $m…
Exact Minimum Distance of the Ding--Li--Xia Cyclic Codes
Yutong Zhang, Yaoran Yang
The cyclic codes introduced by Ding, Li, and Xia form a nonbinary generalization of punctured binary Reed--Muller codes. Ding, Li, and Xia established the bounds $(q^…
Hyperplane anti-Bertini embeddings over finite fields
Yutong Zhang, Yaoran Yang
Baker asked, as recorded by Poonen, whether a fixed smooth quasiprojective variety over a finite field must have a smooth rational hyperplane section after every sufficiently high-…
Finite and Urysohn obstructions to Sabok's S-prime simplex questions
Yutong Zhang, Yaoran Yang
Sabok asked whether the compact convex set \(S'(X)\) attached to a separable metric space of diameter at most one is always a simplex, and whether \(S'(\mathbb U_1)\) is the Poulse…