We provide a streamlined elaboration on existing ideas that link Ising anyon (or equivalently, Majorana) stabilizer codes to certain classes of binary classical codes. The groundwork for such Majorana-based quantum codes can be found in earlier works (including, for example, Bravyi (arXiv:1004.3791) and Vijay et al. (arXiv:1703.00459)), where it was observed that commuting families of fermionic (Clifford) operators can often be systematically lifted from weakly self-dual or self-orthogonal binary codes. Here, we recast and unify these ideas into a classification theorem that explicitly shows how q-isotropic subspaces in $\mathbb{F}_2^{2n}$ yield commuting Clifford operators relevant to Ising anyons, and how these subspaces naturally correspond to punctured self-orthogonal codes in $\mathbb{F}_2^{2n+1}$.

翻译：我们对现有思想进行了简明阐述，这些思想将伊辛任意子（或等价地，马约拉纳费米子）稳定子码与某些类别的二元经典码联系起来。此类基于马约拉纳的量子码的基础工作可见于早期文献（例如 Bravyi (arXiv:1004.3791) 和 Vijay 等人 (arXiv:1703.00459)），其中观察到费米子（Clifford）算符的交换族通常可以从弱自对偶或自正交二元码中系统地提升出来。在此，我们重新表述并统一了这些思想，形成一个分类定理，该定理明确展示了 $\mathbb{F}_2^{2n}$ 中的 q-各向同性子空间如何产生与伊辛任意子相关的交换 Clifford 算符，以及这些子空间如何自然地对应于 $\mathbb{F}_2^{2n+1}$ 中的穿孔自正交码。