Hongfeng Wu

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20242026

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9 papers · 1 filter

math.NT2026

Covering finite fields by translates of multiplicative subgroups

Juncheng Zhou, Hongfeng Wu

Let $G_{d}$ be the subgroup of index $d > 1$ in $F_{q}^{\times}$ , and put $G_{d}^{0} = G_{d} \cup {0}$ . For a covering $A + G_{d}^{0} = F_{q}$ with $# A = s$ , we prove $q \leq d^{8 s / d}$ by shi…

math.NT2026

The Optimal Coefficients-Based Criterion for Primitive Quadratic Polynomials over Finite Fields

Li Zhu, Hongfeng Wu

Let $F_{q}$ be a finite field and consider quadratic polynomials $f (X) = X^{2} + b X + c \in F_{q} [X]$ with primitive constant term $c$ . We construct an optimal coefficients-based…

math.NT2026

Consecutive non-square non-primitive tuples in finite fields

Juncheng Zhou, Hongfeng Wu

Let $q$ be an odd prime power and put \[ θ_q=\frac{φ(q-1)}{q-1}. \] An element of $\Fq$ is called non-square non-primitive, or \emph{NSNP}, if it is both a non-square and a non-pri…

math.NT2026

Primitive Quadratic Polynomials in Additive Coset Families

Juncheng Zhou, Hongfeng Wu

Let $q$ be an odd prime power. For $μ\in\mathbb F_q^\times$ and an additive coset $\barα\in\mathbb F_{q^2}/\mathbb F_q$, consider the family \[ \{x^2+μx-α:α\in\barα\}, \] whe…

math.NT2026

Finite fields whose members are the sum of a potent and a 5-potent

Juncheng Zhou, Peter V. Danchev, Hongfeng Wu

We show that there are only finitely many finite fields whose members are the sum of an $n$ -potent element and a $5$ -potent element. Combining this with the algorithmic results pro…

math.NT2025

The Minimal Binomial Multiples of Polynomials over Finite Fields

Li Zhu, Hongfeng Wu

Let $f (X)$ be a nonconstant polynomial over $F_{q}$ , with a nonzero constant term. The order of $f (X)$ is a classical notion in the theory of polynomials over finite field…

math.NT2025

Cyclotomy, cyclotomic cosets and arithmetic properties of some families in $\frac{F _{l} [ x ]}{⟨ x ^{p^{s} q^{t}} - 1 ⟩}$

Juncheng Zhou, Hongfeng Wu

Arithmetic properties of some families in $\frac{F _{l} [ x ]}{⟨ x ^{p^{s} q^{t}} - 1 ⟩}$ are obtained by using the cyclotomic classes of order 2 with respect to $n = p^{s} q^{t}$ ,…

math.NT2025

The Multiple Equal-Difference Structure of Cyclotomic Cosets

Li Zhu, Juncheng Zhou, Jinle Liu +1

In this paper we introduce the definition of equal-difference cyclotomic coset, and prove that in general any cyclotomic coset can be decomposed into a disjoint union of equal-diff…

math.NT2024

Explicit Representatives and Sizes of Cyclotomic Cosets II: Cyclotomic Systems and Applications to Constacyclic Codes

Li Zhu, Hongfeng Wu

Let $q = p^{e}$ be a prime power, let $ℓ$ be a prime with $g cd (ℓ, q n) = 1$ , and let $n$ be a positive integer. While $q$ -cyclotomic cosets are usually considered modulo a fixed int…

Covering finite fields by translates of multiplicative subgroups

The Optimal Coefficients-Based Criterion for Primitive Quadratic Polynomials over Finite Fields

Consecutive non-square non-primitive tuples in finite fields

Primitive Quadratic Polynomials in Additive Coset Families

Finite fields whose members are the sum of a potent and a 5-potent

The Minimal Binomial Multiples of Polynomials over Finite Fields

Cyclotomy, cyclotomic cosets and arithmetic properties of some families in ⟨xpsqt−1⟩Fl​[x]​

The Multiple Equal-Difference Structure of Cyclotomic Cosets

Explicit Representatives and Sizes of Cyclotomic Cosets II: Cyclotomic Systems and Applications to Constacyclic Codes

Cyclotomy, cyclotomic cosets and arithmetic properties of some families in $\frac{F _{l} [ x ]}{⟨ x ^{p^{s} q^{t}} - 1 ⟩}$