From the 1 of 9 linked papers with an AI index.
9 papers
Schur--Plucker Geometry of the MDS Locus for Principal-Ideal Codes
Yangcheng Li, Pingzhi Yuan
Let \(g\) be a monic polynomial of degree \(r<n\), and let \(C_g(n)\) be the coefficient-vector code formed by multiples \(ug\) with \(°(ug)<n\). We study the coefficient-space MD…
Cyclic Projective Orbits on Rational Normal Curves and MDS Codes
Yangcheng Li, Pingzhi Yuan
The paper characterizes when cyclic Krylov codes form MDS orbit segments on rational normal curves, classifies generalized Reed–Solomon codes via the action of PGL₂, describes the…
Cyclic Codes and Cyclically Covering Subspaces over Finite Fields
Yangcheng Li, Pingzhi Yuan
Let \(q\) be a power of a prime \(p\), and let \(n\) be a positive integer. A subspace \(U\subseteq \mathbb F_q^n\) is called cyclically covering if the union of all its cyclic shi…
Discrete Fourier Transform Approach to Cyclically Covering Subspaces of
Yangcheng Li, Pingzhi Yuan
Let be a prime power and a positive integer. A subspace \( U \subseteq \mathbb{F}_q^n \) is called cyclically covering if the union of all its cyclic shifts covers the whol…
The Arithmetic Geometry of Square-Sided Heron Triangles
Yangcheng Li
We study rational Heron triangles with two marked square sides using elliptic curves and K3 surfaces. An explicit quartic-to-elliptic correspondence parametrizes marked similarity…
On cyclically covering subspaces of
Yangcheng Li, Pingzhi Yuan, Shuang Li +1
For a prime power \( q \) and a positive integer \( n \), a subspace \( U \subseteq \mathbb{F}_q^n \) is called cyclically covering if the union of all its cyclic shifts covers the…