Constructions of codebooks based on additive characters

Codebooks possessing optimal correlation property are utilized to differentiate signals among various users in code-division multiple-access (CDMA) systems. In this paper, a class of codebooks is proposed based on additive characters over finite fields and is verified to be optimal with respect to the Levenshtein bound. By shortening the length of the presented optimal codebooks, a kind of asymptotically optimal codebooks is obtained. To our knowledge, the presented asymptotically optimal codebooks have new parameters. Further more, these optimal and asymptotically optimal codebooks are highly desirable in synchronous Direct-Sequence CDMA systems, as they facilitate the expansion of subscriber capacity within the constrained spectral resources.