11 papers
On binomial order and primitivity of irreducible quadratic polynomials over finite fields
Li Zhu, Hongfeng Wu
In this note we study binomial orders and coefficient criteria for primitive quadratic polynomials over finite fields. First, we introduce Lucas sequences associated with irreducib…
Primitive Quadratic Polynomials in Additive Coset Families
Juncheng Zhou, Hongfeng Wu
The paper proves the Gow–McGuire conjecture on primitive quadratic polynomials over finite fields for all odd prime powers greater than 204,931, using character-sum estimates, refi…
Consecutive non-square non-primitive tuples in finite fields
Juncheng Zhou, Hongfeng Wu
Let be an odd prime power and put \[ θ_q=\frac{Ï(q-1)}{q-1}. \] Let denote a finite field with elements, an element of is called non-square…
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…
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…
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…