15 papers
Support periods of polynomials and support-primitive decomposition of constacyclic codes over Galois rings
Li Zhu, Hongfeng Wu
Let \(A=\GR(p^e,r)\) have residue field \(\F_q\), and let \(λ\in A^\times\). We relate coefficient compression of monic divisors of \(X^N-λ\) to support-primitive decomposition of…
Covering finite fields by translates of multiplicative subgroups
Juncheng Zhou, Hongfeng Wu
Let be the subgroup of index in , and put . For a covering with , we prove by shi…
Affine Symmetries of Polynomial Roots with Multiplicities and Applications to Constacyclic Codes
Li Zhu, Hongfeng Wu
Let be a polynomial over a finite field, and let its defining function record the multiplicities of its roots. In this paper, we introduce the affine stabilizer group and th…
Peirce Stability of Null Polynomials and a Sharp Radical Bound for Finite Rings
Hongfeng Wu
Let be a finite associative ring with identity, and let $\Nul(R)$ denote the set of polynomials in a central indeterminate that vanish identically on under right evaluation…
The Optimal Coefficients-Based Criterion for Primitive Quadratic Polynomials over Finite Fields
Li Zhu, Hongfeng Wu
Let be a finite field and consider quadratic polynomials with primitive constant term . We construct an optimal coefficients-based…
Consecutive non-square non-primitive tuples in finite fields
Juncheng Zhou, Hongfeng Wu
Let 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…
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…
BCH and LCD cyclic codes of length over finite fields
Jinle Liu, Hongfeng Wu, Li Zhu
BCH and LCD cyclic codes of length with are studied. A complete characterization of -cyclotomic cosets modulo is given: Theorem \ref{th4} provides a…
The Arithmetic Singleton Bound on the Hamming Distances of Simple-rooted Constacyclic Codes over Finite Fields
Li Zhu, Hongfeng Wu
In this work, We introduce a new upper bound on the Hamming distance of simple-root constacyclic codes over finite fields, which we call the arithmetic Singleton bound. The main te…
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 -potent element and a -potent element. Combining this with the algorithmic results pro…
The Minimal Binomial Multiples of Polynomials over Finite Fields
Li Zhu, Hongfeng Wu
Let be a nonconstant polynomial over , with a nonzero constant term. The order of is a classical notion in the theory of polynomials over finite field…
Cyclotomy, cyclotomic cosets and arithmetic properties of some families in
Juncheng Zhou, Hongfeng Wu
Arithmetic properties of some families in are obtained by using the cyclotomic classes of order 2 with respect to ,…
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…
Explicit Representatives and Sizes of Cyclotomic Cosets II: Cyclotomic Systems and Applications to Constacyclic Codes
Li Zhu, Hongfeng Wu
Let be a prime power, let be a prime with , and let be a positive integer. While -cyclotomic cosets are usually considered modulo a fixed int…
Explicit Representatives and Sizes of Cyclotomic Cosets and their Application to Cyclic Codes over Finite Fields
Li Zhu, Jinle Liu, Hongfeng Wu
Cyclotomic coset is a classical notion in the theory of finite field which has wide applications in various computation problems. Let be a prime power, and be a positive in…