9 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…
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…
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…
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…
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 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…