Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound

Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks introduced, whose asymptotically achieve corresponding Welch bound and Levenshtein bound. Specially, a class optimal respect is obtained. These constructed by selecting certain rows deterministically circulant matrices, Fourier matrices Hadamard respectively. The construction methods parameters some provided paper new.