Asymptotically optimal codebooks are a family of codebooks that can approach an optimal codebook meeting the Welch bound when the lengths of codewords are large enough. They can be constructed easily and are a good alternative for optimal codebooks in many applications. In this paper, we construct a new class of asymptotically optimal codebooks by using the product of some special finite fields and almost difference sets, which are composed of cyclotomic classes of order eight.
Almost difference sets from Singer type Golomb rulers
