5 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…
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…