High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures

Koki Okada, Kenta Kasai (Apr 23 2026).

Abstract: We construct a quantum low-density parity-check code family from a length-512 Calderbank-Shor-Steane base matrix pair. The base pair is $(3,8)$-regular, both Tanner graphs have girth 8 , and the base code has parameters $[[512,174,8]]$. The construction uses affine cosets of six 3-dimensional subspaces of $\mathbb{F}_2^9$ as check supports, and then applies circulant permutation matrix (CPM) lifts. The main decoding experiment uses the CPM-lifted code with lift factor $P=32$, which has parameters $[[16384, 4142, \leq 40]]$, under the code-capacity depolarizing model. A belief-propagation decoder with post-processing achieved frame error rate about $10^{-8}$ at $p=$ 0.085 , and one observed logical residual of weight 40 gives a decoder-derived upper bound $d \leq 40$.

Arxiv: https://arxiv.org/abs/2604.20838