广义扭Gabidulin码的核与自同构群
Nuclei and automorphism groups of generalized twisted Gabidulin codes
摘要：
广义扭Gabidulin码是有限域上已知的为数不多的最大秩矩阵码之一。作为m × n矩阵的一个子集，当m=n时，任何广义扭Gabidulin码的自同构群最近已被完全确定.在本文中，我们考虑同样的问题，m<n。在一定的参数条件下，我们确定了它们的中核和右核，它们是秩度量码等价的重要不变量。此外，我们还利用它们导出了广义扭Gabidulin码自同构的必要条件.
英文摘要：
Generalized twisted Gabidulin codes are one of the few known families of maximum rank matrix codes over finite fields. As a subset of m by n matrices, when m=n, the automorphism group of any generalized twisted Gabidulin code has been completely determined recently. In this paper, we consider the same problem for m<n. Under certain conditions on their parameters, we determine their middle nuclei and right nuclei, which are important invariants with respect to the equivalence for rank metric codes. Furthermore, we also use them to derive necessary conditions on the automorphisms of generalized twisted Gabidulin codes.
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。
