  In this paper we consider a new normalization of matrices obtained by
choosing distinct codewords at random from linear codes over finite fields and
find that under some natural algebraic conditions of the codes their empirical
spectral distribution converges to Wigner's semicircle law as the length of the
codes goes to infinity. One such condition is that the dual distance of the
codes is at least 5. This is analogous to previous work on the empirical
spectral distribution of similar matrices obtained in this fashion that
converges to the Marchenko-Pastur law.
