LCPs of Subspace Codes

TL;DR

This paper introduces and characterizes linear complementary pairs (LCPs) of subspace codes, providing conditions for their existence, construction methods, and an application to insertion error correction.

Contribution

It defines LCPs for subspace codes, offers a characterization, sufficient existence conditions, construction techniques, and an application in error correction.

Findings

Characterization of subspace codes forming LCPs

Sufficient conditions for LCP existence based on complement functions

Construction methods and application to insertion error correction

Abstract

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.