Stabiliser codes over fields of even order

• URL: http://arxiv.org/abs/2401.06618v2
• Date: Mon, 9 Sep 2024 12:39:40 GMT
• Title: Stabiliser codes over fields of even order
• Authors: Simeon Ball, Edgar Moreno, Robin Simoens,
• Abstract summary: We describe stabiliser codes on n quqits with local dimension q=2h and binary stabiliser codes on hn qubits. A stabiliser code over a field of even order corresponds to a so-called quantum set of symplectic polar spaces.
• Score: 2.048226951354646
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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