Stabilizer codes over fields of even order
- Author
- Simeon Ball, Edgar Moreno and Robin Simoens (UGent)
- Organization
- Project
- 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
- Codes, Qubit, Stabiliser code, Quantum error-correction, Symplectic polar space, Quantum computing, error correction, geometry, QUANTUM-ERROR-CORRECTION
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JN3NZQZ1XQZE39CG6HXTPPPG
- MLA
- Ball, Simeon, et al. “Stabilizer Codes over Fields of Even Order.” IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 71, no. 5, 2025, pp. 3707–18, doi:10.1109/tit.2024.3454480.
- APA
- Ball, S., Moreno, E., & Simoens, R. (2025). Stabilizer codes over fields of even order. IEEE TRANSACTIONS ON INFORMATION THEORY, 71(5), 3707–3718. https://doi.org/10.1109/tit.2024.3454480
- Chicago author-date
- Ball, Simeon, Edgar Moreno, and Robin Simoens. 2025. “Stabilizer Codes over Fields of Even Order.” IEEE TRANSACTIONS ON INFORMATION THEORY 71 (5): 3707–18. https://doi.org/10.1109/tit.2024.3454480.
- Chicago author-date (all authors)
- Ball, Simeon, Edgar Moreno, and Robin Simoens. 2025. “Stabilizer Codes over Fields of Even Order.” IEEE TRANSACTIONS ON INFORMATION THEORY 71 (5): 3707–3718. doi:10.1109/tit.2024.3454480.
- Vancouver
- 1.Ball S, Moreno E, Simoens R. Stabilizer codes over fields of even order. IEEE TRANSACTIONS ON INFORMATION THEORY. 2025;71(5):3707–18.
- IEEE
- [1]S. Ball, E. Moreno, and R. Simoens, “Stabilizer codes over fields of even order,” IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 71, no. 5, pp. 3707–3718, 2025.
@article{01JN3NZQZ1XQZE39CG6HXTPPPG,
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.}},
author = {{Ball, Simeon and Moreno, Edgar and Simoens, Robin}},
issn = {{0018-9448}},
journal = {{IEEE TRANSACTIONS ON INFORMATION THEORY}},
keywords = {{Codes,Qubit,Stabiliser code,Quantum error-correction,Symplectic polar space,Quantum computing,error correction,geometry,QUANTUM-ERROR-CORRECTION}},
language = {{eng}},
number = {{5}},
pages = {{3707--3718}},
title = {{Stabilizer codes over fields of even order}},
url = {{http://doi.org/10.1109/tit.2024.3454480}},
volume = {{71}},
year = {{2025}},
}
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