Abstract:

Finite-length bivariate-bicycle (BB) quantum LDPC codes are attractive low-overhead memory candidates, but typical design methods consider only a scalar cover factor. We introduce a directionally shifted-cover design rule that treats both the split h = ax * ay and the monomial lift offsets as optimization variables. The novelty is a short-cycle net-voltage criterion. Support-difference equality defines a base Tanner 4-cycle in the base polynomial pair, which is assigned voltages in Gh = Zax * Zay; zero voltage lets the corresponding small base Tanner cycle or closed walk return to the starting lifted vertex after one traversal, whereas nonzero high-order voltage forces it to close after r traversals, where r is the net-voltage order. This criterion provides an interpretable prefilter before exact distance verification and explains why cover direction matters at fixed length. For a (6, 6) base and h = 4, the optimized pure y-cover gives [[288, 20, 18]], improving kd ^ 2 / n over the optimized pure x-cover [[288, 16, 18]].