  In this paper, using additive characters of finite field, we find a codebook
which is equivalent to the measurement matrix in [20]. The advantage of our
construction is that it can be generalized naturally to construct the other
five classes of codebooks using additive and multiplicative characters of
finite field. We determine the maximal cross-correlation amplitude of these
codebooks by the properties of characters and character sums. We prove that all
the codebooks we constructed are asymptotically optimal with respect to the
Welch bound. The parameters of these codebooks are new.
