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.

众所周知，秩度量中最优反码的维数可以被矩阵的行数和列数之间的最大值m整除。此外，对于可被m整除的固定k，最佳秩度量反码是维度k中具有最小最大秩的代码。在本文中，我们研究了维数不能被m整除的秩度量码族根据 Anticode 边界，其最大等级对于该维度的代码可能是最低的。由于这些不是最优反代码，我们称它们为准最优反代码 (qOAC)。另外，我们称对偶qOAC为qOAC，其对偶也是qOAC。我们明确描述了对偶 qOAC 的结构，并计算了它们的权重分布、广义权重和相关的q -多边形矩阵。