  We investigate the asymptotic density of error-correcting codes with good
distance properties and prescribed linearity degree, including sublinear and
nonlinear codes. We focus on the general setting of finite
translation-invariant metric spaces, and then specialize our results to the
Hamming metric, to the rank metric, and to the sum-rank metric. Our results
show that the asymptotic density of codes heavily depends on the imposed
linearity degree and the chosen metric.
