论文标题
准最佳动物：结构和不变性
Quasi optimal anticodes: structure and invariants
论文作者
论文摘要
众所周知，排名中的最佳二端的尺寸除以矩阵的行数和列之间的最大值。此外，对于固定的k被M可除以M，最佳秩式二极管是级别k的代码最小级别的代码。在本文中，我们研究了级别代码的家族，其维度不可分由M排除，并且根据抗模拟的界限，其最大等级是该维度的最大等级。由于这些不是最佳的抗体，因此我们称它们为准最佳抗体（QOAC）。此外，我们将双重QOAC称为QOAC，其双重二值也是QOAC。我们明确地描述了双重QOAC的结构，并计算其重量分布，广义重量和相关的Q-脊椎动物。
It is well-known that the dimension of optimal anticodes in the rank-metric is divisible by the maximum m between the number of rows and columns of the matrices. Moreover, for a fixed k divisible by m, optimal rank-metric anticodes are the codes with least maximum rank, among those of dimension k. In this paper, we study the family of rank-metric codes whose dimension is not divisible by m and whose maximum rank is the least possible for codes of that dimension, according to the Anticode bound. As these are not optimal anticodes, we call them quasi optimal anticodes (qOACs). In addition, we call dually qOAC a qOAC whose dual is also a qOAC. We describe explicitly the structure of dually qOACs and compute their weight distributions, generalized weights, and associated q-polymatroids.
