The non-existence of a [[13,5,4]] quantum stabilizer code

TL;DR

This paper proves that a specific quantum stabilizer code with parameters [[13,5,4]] cannot exist, resolving a long-standing open problem in quantum coding theory.

Contribution

It provides a definitive proof of the non-existence of the [[13,5,4]] quantum stabilizer code, settling a long-standing question.

Findings

Proves the non-existence of the [[13,5,4]] quantum stabilizer code.

Closes a long-standing open problem in quantum coding theory.

Provides insights into the limitations of quantum stabilizer codes.

Abstract

We solve one of the oldest problems in the theory of quantum stabilizer codes by proving the non-existence of quantum [[13,5,4]]-codes.