A New Construction of Codebooks Meeting the Levenshtein Bound

Codebooks with low coherence have extensive applications in many fileds such as code division multiple access (CDMA) communication systems, MIMO communications, compressed sensing and so on. In this paper, based on additive characters over finite fields, we propose a construction of optimal codebook with respect to the Levenshtein bound and verify that it is a new construction. By shortening the length of the optimal codebooks, we present a construction of codebooks asymptotically meeting the Levenshtein bound. To the best of our knowledge, the parameters of the asymptotically optimal codebooks are new.