The files linked from the binary CSS LDPC table contain the affine-permutation parameters used to build the \(H_X\) and \(H_Z\) parity-check matrices. Each file defines a family member with a specific lift size \(P\), regularity \((J,L)=(3,12)\), and a current structural upper bound on the minimum distance.
The first lines encode the construction parameters and the affine maps.
216 3 12 17265506054090875 181 91 37 181 91 37 105 57 192 186 57 156 193 97 193 181 97 193 112 116 64 54 44 100
The first line is \(P\), \(J\), and \(L\). The second line is the random seed used by the search program. The next three lines are the multiplicative and additive coefficients defining the affine permutation maps \(f_i(x)=a_i x+b_i \bmod P\) and \(g_i(x)=c_i x+d_i \bmod P\).
The remaining lines start with # and summarize the best structural certificates currently known
for that file.
# distance_bound_overall 14 # latent_x_upper 24 # latent_z_upper 24 # nonlatent_x_upper 42 # nonlatent_z_upper 36 # decoderlog_z_upper 14
The most important fields are:
distance_bound_overall: the current best upper bound on the quantum minimum distance.latent_*: upper bounds coming from the latent-space witness construction.nonlatent_*: upper bounds from \(m\)-block row-space-external witnesses.cycle8_ets_*: upper bounds found by the cycle-8 ETS search, when available.decoderlog_*: upper bounds extracted from decoder failures that produced a syndrome-matched non-stabilizer residual; entries such as decoderlog_z_support list the support positions of the witness.ub48 means that, at the time the file was
written, the best known overall upper bound was 48. Later experiments can improve that number, so the summary
comments inside the file should be treated as the authoritative source.
If a file is listed on the main page as \(\left[\left[n,k,\leq u\right]\right]\), then \(n=12P\), \(k\) is the CSS code dimension computed from the ranks of \(H_X\) and \(H_Z\), and \(u\) is the smallest currently certified upper bound among the available witnesses.
These files are updated as our search and certification pipeline evolves, so the published table on the main page should be understood as a living record rather than a frozen final benchmark.