6 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…
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…
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…
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 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…