Work

Stabiliser codes over fields of even order

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2401.06618

Authors: Ball, Simeon, Moreno, Edgar, Simoens, Robin

Institutions: Ghent University, Universitat Politècnica de Catalunya

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, Ministerio de Ciencia e Innovación, Vlaamse regering, Universitat Politècnica de Catalunya, Agencia Estatal de Investigación

Awards: G1855990336, G2262748287, G3480869486, G425668148, G4538077655, G5421974903, G5805502524, Applications of finite geometry in spectral graph theory and in classical and quantum error-correction, G8250324087

OpenAlex ID: W4390897852

Cites:

Cited by:

Related to: 10