Constructions of self-orthogonal and LCD subspace codes

TL;DR

This paper introduces new methods for constructing self-orthogonal and LCD subspace codes using various combinatorial and algebraic structures, expanding the toolkit for code design in information theory.

Contribution

It provides novel construction techniques for self-orthogonal and LCD subspace codes from matrices and combinatorial designs, under specific conditions.

Findings

Constructed codes from mutually quasi-unbiased weighing matrices.

Developed codes from linked systems of symmetric designs.

Established connections with Deza graphs and equitable partitions.

Abstract

Recently, the notions of self-orthogonal subspace codes and LCD subspace codes were introduced, and LCD subspace codes obtained from mutually unbiased weighing matrices were studied. In this paper, we provide a method of constructing self-orthogonal and LCD subspace codes from a set of matrices under certain conditions. In particular, we give constructions of self-orthogonal and LCD subspace codes from mutually quasi-unbiased weighing matrices, linked systems of symmetric designs, and linked systems of symmetric group divisible designs, Deza graphs and their equitable partitions.