7 papers · 1 filter
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…
Cyclic Projective Orbits on Rational Normal Curves and MDS Codes
Yangcheng Li, Pingzhi Yuan
Let \(A\) be a cyclic operator on an \(r\)-dimensional vector space over a field \(k\), and let \(z\) be a cyclic vector. Their Krylov code has parity-check matrix \((z,Az,\ldots,A…
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…
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…
Determination of Some Types of Permutations over with Low-Degree
Xuan Pang, Yangcheng Li, Pingzhi Yuan +1
The characterization of permutations over finite fields is an important topic in number theory with a long-standing history. This paper presents a systematic investigation of low-d…
Permutation polynomials of the form
Yangcheng Li, Xuan Pang, Pingzhi Yuan +1
Given a polynomial \( H(x) \) over \(\mathbb{F}_{q^n}\), we study permutation polynomials of the form \( x + γ\mathrm{Tr}(H(x)) \) over \(\mathbb{F}_{q^n}\). Let \[P_H=\{γ\in \math…