Exact distances for 1027 bivariate-bicycle codes and a coset upper bound

A bivariate-bicycle (BB) code is defined by two polynomials A, B over F2[x,y]/(x^l - 1, y^m - 1) and has n = 2lm qubits. We fix the polynomials in two families and vary only (l, m) with n <= 400, and report the exact distance of 1027 codes. We then give an upper bound on the distance, built from logicals confined to unions of shifted cosets of a cyclic subgroup H in each block (r <= 2 for every H, and r = 3 when the number of cosets is at most 12), and compare it with the data. It equals the exact distance on 1014 of the 1027 codes (an in-sample fit that is not blind). Two blind tests were run with the predictor and predictions hashed before any distance was read. On 25 distinct catalogued codes it is tight on 24 (96%). On 150 random weight-6 BB codes it is tight on only 102 (68%, 95% confidence interval 0.599-0.754), which fails the preregistered criterion of at least 90%. The bound is never below the exact distance in either test. The bound is therefore tight on 24 of 25 catalogued codes but not on random codes, and the empirical conjecture of Section 5 is restricted to the two families studied.