  We study sequences of linear or affine codes with uniform weight spectrum,
i.e., a part of codewords with any fixed weight tends to zero. It is proved
that a sequence of linear codes has a uniform weight spectrum if the number of
vectors from codes with weight $1$ grows to infinity. We find an example of a
sequence of linear codes such that the dimension of the code is the half of the
codelength but it has not a uniform weight spectrum. This example generates
eigenfunctions of the Fourier transform with minimal support and partial
covering sets. Moreover, we generalize some MacWilliams-type identity.
  Keywords: weight distribution of code, dual code, MacWilliams identity,
Fourier transform, partial covering array
