Primitive Idempotents and Constacyclic Codes over Finite Chain Rings

Skew cyclic and skew $(α_1 + uα_2 + vα_3 + uvα_4)$-constacyclic codes over $F_q + uF_q + vF_q + uvF_q$

In this note, we study skew cyclic and skew constacyclic codes over the ring $\mathcal{R}=F_{q}+uF_{q}+vF_{q}+uvF_{q}$ where $q=p^{m},$ $p$ is an odd prime, $u^{2}=u,~v^{2}=v,~uv=vu$. We show that Gray images of a skew cyclic and skew $α$-constacyclic code of length $n$ are skew quasi-cyclic code of length $4n$ over $F_{q}$ of index 4. Also, it is shown that skew $α$-constacyclic codes are either equivalent to $α$-constacyclic codes or $α$-quasi-twisted codes over $\mathcal{R}$. Further, structural properties, specially, generating polynomials and idempotent generators for skew cyclic and skew…

有限链环上的二维常循环码

Two-dimensional constacyclic codes over finite chain rings

研究有限链环上二维\((\lambda,\mu)\)-常循环码的代数结构，通过分析本原幂等元确定码的生成元以获其结构，还找出二维常循环码在有限链环上关于秩是最大汉明距离的条件。

有限交换链环上的LCD码与自正交扭曲群码

LCD and self-orthogonal twisted group codes over finite commutative chain rings

本文研究有限交换链环上的k-Galois LCD常循环群码，利用扭曲群环结构通过幂等生成元和经典对合刻画该类码，还找到部分优良LCD码。

来自扭群代数的优质码

Good codes from twisted group algebras

该研究证明有限交换环上常循环码可实现为扭群环的理想，研究了码间等距与有限域上k-Galois LCD常循环码，刻画了欧几里得内积下常循环LCD码并找到优质码。

Primitive idempotents in central simple algebras over $\mathbb{F}_q(t)$ with an application to coding theory

We consider the algorithmic problem of computing a primitive idempotent of a central simple algebra over the field of rational functions over a finite field. The algebra is given by a set of structure constants. The problem is reduced to the computation of a division algebra Brauer equivalent to the central simple algebra. This division algebra is constructed as a cyclic algebra, once the Hasse invariants have been computed. We give an application to skew constacyclic convolutional codes.

仿射代数环上常循环码的Galois包络

Galois hulls of constacyclic codes over affine algebra rings

该研究针对仿射代数环上的λ-常循环码，定义了k-Galois内积，推导了其k-Galois对偶码、包络的生成元形式与包络维数公式，给出k-Galois LCD码的判定条件，并展示了其在纠缠辅助量子纠错码构造中的应用。