Quantum CSS LDPC Codes with Quasi-Dyadic Structure

Quantum quasi-cyclic (QC) and quantum low-density parity-check (LDPC) codes have received significant attention due to their algebraic regularity and performance under low-complexity decoding. In this work, we explore a class of structured quantum codes based on reproducible matrices, which generalize known families such as cyclic, QC, and dyadic codes. Focusing on sparse quasi-dyadic (QD) structures, we investigate how their symmetries influence Tanner graph cycles. Moreover, we construct quantum LDPC codes within the Calderbank-Shor-Steane (CSS) framework, analyzing dual-containing configurations, and assess their error rates.