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Recently we considered a class of random matrices obtained by choosingdistinct codewords at random from linear codes over finite fields and provedthat under some natural algebraic conditions their empirical spectraldistribution converges to Wigner's semicircle law as the length of the codesgoes to infinity. One of the conditions is that the dual distance of the codesis at least 5. In this paper, employing more advanced techniques related toStieltjes transform, we show that the dual distance being at least 5 issufficient 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.

Random Matrices from Linear Codes and Wigner's Semicircle Law II