This paper investigates certified upper bounds on the minimum distance of an explicit family of Calderbank-Shor-Steane quantum LDPC codes constructed from affine permutation matrices. All codes considered here have active Tanner graphs of girth eight. Rather than attempting to prove a general lower bound for the full code distance, we focus on constructing low-weight non-stabilizer logical representatives, which yield valid upper bounds once they are verified to lie in the opposite parity-check kernel and outside the stabilizer row space. We develop a unified framework for such witnesses arising from latent row relations, restricted-lift subspaces including block-compressed, selected-fiber, and CRT-stripe constructions, cycle- 8 elementary trapping-set structures, and decoder-failure residuals. In every case, search is used only to generate candidates; the reported bounds begin only after explicit kernel and row-space exclusion tests have been passed. For the latent part, we also identify a block-compression criterion under which the certification becomes exact. Applying these methods to representative APM-LDPC codes sharpens previously reported upper bounds and provides concrete certified values across the explored parameter range.

翻译：本文研究了一类由仿射置换矩阵构造的Calderbank-Shor-Steane量子LDPC码最小距离的认证上界。本文考虑的所有码字均具有围长为八的有效Tanner图。我们并未尝试证明全码距离的通用下界，而是聚焦于构造低权重的非稳定子逻辑代表元——一旦这些代表元被验证位于对偶校验核中且不在稳定子行空间中，即可得到有效的上界。我们建立了一个统一框架来刻画此类见证者，其来源包括：隐含行关系、受限升子空间（含块压缩、选定纤维及CRT-条纹构造）、环-8基本陷阱集结构，以及译码失败残差。在所有情况下，搜索仅用于生成候选者；报告的上界均始于显式的核与行空间排除测试通过之后。对于隐含部分，我们还识别出一种块压缩准则，在该准则下认证过程可实现精确化。将这些方法应用于代表性APM-LDPC码，不仅优化了先前报告的上界，还在所探索的参数范围内提供了具体的认证值。