Bias-tailored codes such as the XZZX surface code and the domain wall color code achieve high dephasing-biased thresholds because, in the infinite-bias limit, their $Z$ syndromes decouple into one-dimensional repetition-like chains; the $X^3Z^3$ Floquet code shows an analogous strip-wise structure for detector events in spacetime. We capture this common mechanism by defining strip-symmetric biased codes, a class of static stabilizer and dynamical (Floquet) codes for which, under pure dephasing and perfect measurements, each elementary $Z$ fault is confined to a strip and the Z-detector--fault incidence matrix is block diagonal. For such codes the Z-detector hypergraph decomposes into independent strip components and maximum-likelihood $Z$ decoding factorizes across strips, yielding complexity savings for matching-based decoders. We characterize strip symmetry via per-strip stabilizer products, viewed as a $\mathbb{Z}_2$ 1-form symmetry, place XZZX, the domain wall color code, and $X^3Z^3$ in this framework, and introduce synthetic strip-symmetric detector models and domain-wise Clifford constructions that serve as design tools for new bias-tailored Floquet codes.

翻译：针对偏置噪声设计的编码（如XZZX表面码与畴壁色码）能够实现较高的退相位偏置阈值，这是因为在无限偏置极限下，其$Z$校验子解耦为一维类重复链；$X^3Z^3$ Floquet码在时空检测器事件中表现出类似的条带化结构。我们通过定义条带对称偏置码来捕捉这一共同机制，此类静态稳定子码与动态（Floquet）码在纯退相位与完美测量条件下，每个基本$Z$故障被限制在单一条带内，且Z检测器-故障关联矩阵呈块对角形式。对于此类编码，Z检测器超图可分解为独立的条带分量，最大似然$Z$译码可跨条带分解，从而为基于匹配的译码器带来复杂度降低的优势。我们通过每条带的稳定子乘积（视为$\mathbb{Z}_2$ 1-形式对称性）来刻画条带对称性，将XZZX码、畴壁色码及$X^3Z^3$码纳入此框架，并引入合成条带对称检测器模型与畴级Clifford构造方法，作为设计新型偏置自适应Floquet码的工具。