赋值的秩度量码
Valued rank-metric codes
AI总结：
本文研究离散赋值域上矩阵线性空间的维数与最小秩下降，通过斜代数和Mustafin簇建模秩度量码，给出维数下降的充分条件。
摘要：
本文研究了定义在离散赋值域上的矩阵线性空间，并讨论了它们在与相关剩余域上的维数和最小秩下降。为此，我们通过由环的伽罗瓦扩张导出的斜代数，初步探索了离散赋值环上的秩度量码理论。此外，我们利用Mustafin簇对秩度量码的射影化进行建模，并据此给出维数下降的充分条件。
英文摘要：
In this paper, we study linear spaces of matrices defined over discretely valued fields and discuss their dimension and minimal rank drops over the associated residue fields. To this end, we take first steps into the theory of rank-metric codes over discrete valuation rings by means of skew algebras derived from Galois extensions of rings. Additionally, we model projectivizations of rank-metric codes via Mustafin varieties, which we then employ to give sufficient conditions for a decrease in the dimension.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
