Two families of nearly optimal codebooks

Codebooks are widely applied in code-division multiple-access systems. Recently, several authors constructed codebooks meeting or nearly meeting the Welch bound (i.e. nearly optimal codebooks) using difference set, almost difference set, relative difference set, and so on. In this paper, we will give two families of nearly optimal codebooks. First, we give a class of new almost difference sets and use them to construct nearly optimal codebooks. Second, we present a general construction of codebooks from partial difference sets and obtain several classes of nearly optimal codebooks.

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