  Bosonic error correcting codes utilize the infinite dimensional Hilbert space
of a harmonic oscillator to encode a qubit. Bosonic rotation codes are
characterized by a discrete rotation symmetry in their Wigner functions and
include codes such as the cat and binomial codes.We define two different
notions of random bosonic rotation codes and numerically explore their
performance against loss and dephasing. We find that the best random rotation
codes can outperform cat and binomial codes in a certain parameter regime where
loss is large and dephasing errors are small.
