LCPs of Subspace Codes
This work addresses a theoretical extension in coding theory for subspace codes, but it appears incremental as it adapts existing LCP concepts to a new context.
The paper introduces linear complementary pairs (LCPs) for subspace codes, characterizing them and providing constructions using techniques like complement functions, with an application to insertion error correction.
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.