10 papers · 1 filter
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…