Quantum Gilbert-Varshamov Bound Through Symplectic Self-Orthogonal Codes

TL;DR

This paper establishes a Gilbert-Varshamov bound for symplectic self-orthogonal codes, leading to a new bound for quantum codes, using counting arguments to advance quantum coding theory.

Contribution

It introduces a Gilbert-Varshamov bound for symplectic self-orthogonal codes and derives a new bound for quantum codes, expanding theoretical limits in quantum error correction.

Findings

Derived Gilbert-Varshamov bound for symplectic self-orthogonal codes

Established Gilbert-Varshamov bound for quantum codes

Used counting arguments to achieve bounds

Abstract

It is well known that quantum codes can be constructed through classical symplectic self-orthogonal codes. In this paper, we give a kind of Gilbert-Varshamov bound for symplectic self-orthogonal codes first and then obtain the Gilbert-Varshamov bound for quantum codes. The idea of obtaining the Gilbert-Varshamov bound for symplectic self-orthogonal codes follows from counting arguments.