线性码的随机矩阵与Wigner循环律
Random Matrices from Linear Codes and Wigner's semicircle law
摘要：
本文考虑了从有限域上的线性码中随机选取不同码字所得到的矩阵的一种新的正规化，并发现在某些自然代数条件下，当码长趋于无穷大时，它们的经验谱分布收敛于Wigner循环律。一个这样的条件是码的对偶距离至少为5。这是类似于以前的工作经验谱分布的类似矩阵，以这种方式获得收敛到马琴科-帕斯托尔定律。
英文摘要：
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.
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