发表机构
Università degli Studi di Napoli Federico II; University of South Florida; Pennsylvania State University（那不勒斯费德里科二世大学; 南佛罗里达大学; 宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究从Drinfeld模出发，通过限制有界次数态射到互素挠点构造出超奇异情形下的秩与和秩码，得到显式MSRD族及多项式时间解码器，还推导了对应滤波方程。
AI 中文摘要
我们通过将有界次数的态射限制到与特征互素的挠点，构造了加法秩度量码与和秩度量码。对于特征𝔭（次数为d）下秩为r的超奇异Drinfeld模，态射空间的稳定化公式给出了𝔽_q维数为mrt−c（其中c=r(r−1)(d−1)/2）、最小距离为r−t+1的秩度量码。同时限制到ℓ个不同的次数为m的挠模，得到了具有相同维数、最小距离至少为ℓr−t+1的加法和秩码。它们的归一化Singleton缺陷趋于零，而在特征(T)下，模φ_T=τ^r使缺陷消失，并生成了显式的MSRD族。我们将该族与支撑在中心斜多项式上的斜中国剩余码对应，证明其多斜重量恰好是和秩重量的m倍，这给出了专门的Singleton型界和可达到全和秩唯一解码半径的多项式时间唯一解码器。我们还为一般超奇异和秩构造推导了Welch-Berlekamp型滤波方程，只要相关态射空间的基和限制映射可计算，该方程就成为有效解码器。
英文摘要
We construct additive rank-metric and sum-rank-metric codes from Drinfeld modules by restricting bounded-degree morphisms to prime-to-characteristic torsion. For supersingular Drinfeld modules of rank $r$ in characteristic $\mathfrak{p}$ of degree $d$, the stabilization formula for morphism spaces yields rank-metric codes of $\mathbb{F}_q$-dimension $mrt-c$ and minimum distance $r-t+1$, where $c=r(r-1)(d-1)/2$. Simultaneous restriction to $\ell$ distinct degree-$m$ torsion modules gives additive sum-rank codes of the same dimension and minimum distance at least $\ell r-t+1$. Their normalized Singleton defects tend to zero, while in characteristic $(T)$ the module $ϕ_T=τ^r$ makes the defect vanish and produces an explicit MSRD family. We identify this family with a skew Chinese remainder theorem code supported on central skew polynomials and prove that its poly-skew weight is exactly $m$ times its sum-rank weight. This gives a specialized Singleton-type bound and a polynomial-time unique decoder up to the full sum-rank unique-decoding radius. We also derive a Welch-Berlekamp-type filter equation for the general supersingular sum-rank construction; it becomes an effective decoder whenever bases of the relevant morphism spaces and the restriction maps are computable.
