IRSI two-block qLDPC code [[124,2,16]], 30 September 2026
Published at https://irsi.ai/records.html#qldpc

Code: l = 62, a(z) = 1 + z, b(z) = 1 + z^36 + z^47 + z^54 over F2[z]/(z^62 - 1).
A, B = 62 x 62 circulants of a and b. H_X = [A | B], H_Z = [B^T | A^T]. Every check has weight 6.

check_qldpc_124_2_16.py   Python 3 standard library. Checks H_X H_Z^T = 0, both ranks 61 (so k = 2),
                          check weight 6, and that one X and one Z logical operator of weight 16 exist
                          (so d <= 16). --negctl also runs three broken inputs, which must fail.
                          It does not prove d >= 16.
bz.c                      Brouwer-Zimmermann exhaustive distance search for this family (C, needs gcc or
                          clang with unsigned __int128). It builds the checks itself from the exponents.
                            gcc -O3 -o bz bz.c
                            ./bz 62 X "0 1" "0 36 47 54"     (about 7 s; last line: EXACT d_X=16 ...)
                            ./bz 62 Z "0 1" "0 36 47 54"     (EXACT d_Z=16)
                          After all weight-w combinations in both information sets, every codeword not yet
                          seen has weight >= 2(w+1); it stops at w = 7, when that bound reaches 16.
milp-recompute-124.json   Summary of the independent exact MILP recompute: status, objective and bound of
                          all 12 branches (2 sectors x 3 logical classes x 2 symmetry branches), and the
                          optimal supports. Solver: HiGHS 1.15.1, gap 0. This is a solver log, not a formal
                          proof certificate.

Neither program is formally verified. Contact: peter@irsi.ai
