A subspace code is a nonempty collection of subspaces of the vector space $\mathbb{F}_q^{n}$. A pair of linear codes is called a linear complementary pair (in short LCP) of codes if their intersection is trivial and the sum of their dimensions equals the dimension of the ambient space. In this paper, we introduce the concept of LCPs of subspace codes. We first provide a characterization of subspace codes that form an LCP. Furthermore, we present a sufficient condition for the existence of an LCP of subspace codes based on a complement function on a subspace code. In addition, we give several constructions of LCPs for subspace codes using various techniques and provide an application to insertion error correction.

翻译：子空间码是向量空间$\mathbb{F}_q^{n}$的子空间的一个非空集合。一对线性码被称为线性互补对（简称LCP），如果它们的交集为零子空间，且维数之和等于环境空间的维数。本文引入子空间码的LCP对概念。首先给出构成LCP对的子空间码的刻画，进一步，基于子空间码上的补函数，给出LCP对存在性的一个充分条件。此外，利用多种技巧给出子空间码LCP对的若干构造方法，并展示其在插入错误纠正中的应用。