Quantum low-density parity-check (QLDPC) codes provide a practical balance between error-correction capability and implementation complexity in quantum error correction (QEC). In this paper, we propose an algebraic construction based on dyadic matrices for designing both classical and quantum LDPC codes. The method first generates classical binary quasi-dyadic LDPC codes whose Tanner graphs have girth 6. It is then extended to the Calderbank-Shor-Steane (CSS) framework, where the two component parity-check matrices are built to satisfy the compatibility condition required by the recently introduced CAMEL-ensemble quaternary belief propagation decoder. This compatibility condition ensures that all unavoidable cycles of length 4 are assembled in a single variable node, allowing the mitigation of their detrimental effects by decimating that variable node.

翻译：量子低密度奇偶校验（QLDPC）码在量子纠错（QEC）中提供了纠错能力与实现复杂度之间的实用平衡。本文提出了一种基于dyadic矩阵的代数构造方法，用于设计经典和量子LDPC码。该方法首先生成其Tanner图围长为6的经典二进制准dyadic LDPC码，随后将其扩展至Calderbank-Shor-Steane（CSS）框架。在该框架中，两个分量奇偶校验矩阵被构建以满足近期引入的CAMEL-ensemble四进制置信传播解码器所需的兼容性条件。此兼容性条件确保了所有不可避免的长度为4的环被聚集在单个变量节点中，从而允许通过对该变量节点进行消减来减轻其有害影响。