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.

翻译：我们证明，GF(2^h)与GF(2)^h之间的自然同构引出了局部维数q=2^h的n量子四元组上稳定子码与hn量子比特上二元稳定子码之间的双射。这使我们能够从几何角度描述这些码：偶特征域上的稳定子码对应所谓的辛极空间量子集。此外，等价的稳定子码具有相似的几何结构，这可用于证明[[4,0,3]]_4稳定子码的唯一性，以及[[7,1,4]]_4和[[8,0,5]]_4稳定子码的不存在性。