TWO CLASSES OF NEAR-OPTIMAL CODEBOOKS WITH RESPECT TO THE WELCH BOUND

An (N, K) codebook C is a collection of N unit norm vectors in a K-dimensional vectors space. In applications of codebooks such as CDMA, those vectors in a codebook should have a small maximum magnitude of inner products between any pair of distinct code vectors. In this paper, we propose two constructions of codebooks based on p-ary linear codes and on a hybrid character sum of a special kind of functions, respectively. With these constructions, two classes of codebooks asymptotically meeting the Welch bound are presented.