Generalizing the construction of two-block group algebra (2BGA) codes, we introduce a family of two-block quantum LDPC codes constructed using the action of a group on the cosets of its subgroup. This replaces the regular group actions of the earlier two-block constructions and significantly expands the search space, yielding new quantum LDPC codes outside the 2BGA family. Through a computer search, we identify several new quantum LDPC codes, including weight-6 codes with parameters $[[48,8,6]]$, $[[96,8,10]]$, and $[[224,12,16]]$, as well as weight-8 codes with parameters $[[84,16,8]]$, $[[112,16,10]]$, $[[128,16,12]]$, and $[[168,16,15]]$. Furthermore, we introduce a maximally packed syndrome extraction schedule of depth $w+2$, including initialization and measurement steps, for any code with a maximum stabilizer weight of $w$ from our family. Under a standard circuit-level noise model, our codes, when decoded using BP-OSD, perform competitively with BB codes, achieving thresholds of $\approx0.65\%$ for the weight-6 family and $\approx0.35\%$ for the weight-8 family. Finally, we introduce a group-theoretic framework to generate sequences of graph-based covers of 2BGA codes, recovering and extending recent results on code constructions of this type.

翻译：推广两块群代数（2BGA）码的构造，我们引入一族利用群在其子群陪集上的作用构建的两块量子LDPC码。这取代了早期两块构造中的正则群作用，显著扩展了搜索空间，得到了2BGA族之外的新型量子LDPC码。通过计算机搜索，我们识别出若干新型量子LDPC码，包括参数为$[[48,8,6]]$、$[[96,8,10]]$和$[[224,12,16]]$的权重6码，以及参数为$[[84,16,8]]$、$[[112,16,10]]$、$[[128,16,12]]$和$[[168,16,15]]$的权重8码。此外，我们针对本族中最大稳定子权重为$w$的任意码，引入了一种深度为$w+2$（包括初始化和测量步骤）的最大化紧凑综合征提取方案。在标准电路级噪声模型下，采用BP-OSD解码时，我们的码与BB码性能相当，权重6族和权重8族的阈值分别达到$\approx0.65\%$和$\approx0.35\%$。最后，我们引入了一个群论框架来生成2BGA码的基于图覆盖的序列，恢复并扩展了此类码构造的最新结果。