Stabiliser codes over fields of even order
Combinatorics
2024-09-10 v2 Information Theory
math.IT
Quantum Physics
Abstract
We prove that the natural isomorphism between GF(2^h) and GF(2)^h induces a bijection between stabiliser codes on n quqits with local dimension q=2^h and binary stabiliser codes on hn qubits. This allows us to describe these codes geometrically: a stabiliser code over a field of even order corresponds to a so-called quantum set of symplectic polar spaces. Moreover, equivalent stabiliser codes have a similar geometry, which can be used to prove the uniqueness of a [[4,0,3]]_4 stabiliser code and the nonexistence of both a [[7,1,4]]_4 and an [[8,0,5]]_4 stabiliser code.
Keywords
Cite
@article{arxiv.2401.06618,
title = {Stabiliser codes over fields of even order},
author = {Simeon Ball and Edgar Moreno and Robin Simoens},
journal= {arXiv preprint arXiv:2401.06618},
year = {2024}
}