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…
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…
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…