  We consider the problem of generating symmetric pseudo-random sign (+/-1)
matrices based on the similarity of their spectra to Wigner's semicircular law.
Using binary m-sequences (Golomb sequences) of lengths n=2^m-1, we give a
simple explicit construction of circulant n by n sign matrices and show that
their spectra converge to the semicircular law when n grows. The Kolmogorov
complexity of the proposed matrices equals to that of Golomb sequences and is
at most 2log(n) bits.
