Arda Aydin, Itzhak Tamo, Alexander Barg (Jun 17 2026).
Abstract: 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
≈0.65% for the weight-6 family and
≈0.35% 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.
