Two Classes of Codebooks Nearly Meeting the Welch Bound

In this paper, the value of I_max(C) for codebooks C = C(D) constructed by certain almost difference sets D in F_q^x is determined and expressed in terms of Jacobi sums from which it shows that such codebooks nearly meet the Welch bound. This result is an answer of a question raised by C.Ding and T.Feng in [2]. We also present another series of codebooks which nearly meet the Welch bound, where the codebook is constructed by a subset R = F_q1 ⊕ F_q2. When q₁ = q₂, D_ε is an almost difference set of R.