  Recently we considered a class of random matrices obtained by choosing
distinct codewords at random from linear codes over finite fields and proved
that under some natural algebraic conditions their empirical spectral
distribution converges to Wigner's semicircle law as the length of the codes
goes to infinity. One of the conditions is that the dual distance of the codes
is at least 5. In this paper, employing more advanced techniques related to
Stieltjes transform, we show that the dual distance being at least 5 is
sufficient to ensure the convergence, and the convergence rate is of the form
$n^{-\beta}$ for some $0 < \beta < 1$, where $n$ is the length of the code.

Probability