Asymptotically optimal codebooks based on generalized Jacobi sums

Codebooks with small inner-product correlation are applied in many practical applications including direct spread code division multiple access communications, space-time codes and compressed sensing. It is extremely difficult to construct codebooks achieving the Welch or Levenshtein bound. In this paper, we firstly generalize Jacobi sums over finite fields and secondly obtain asymptotically optimal codebooks with respect to the Welch or Levenshtein bound. Our main results generalize those in [11] and the codebooks in this paper have more flexible parameters than those in [11].