Two New Classes of Codebooks Asymptotically Achieving the Welch Bound

Exponential sums over Galois rings have many applications in coding theory, cryptography and algebraic combinatorics. In this article, we employ additive characters and multiplicative characters over Galois rings to present two classes of codebooks, and prove that these codebooks asymptotically achieve the Welch bound. In addition, the resulting codebooks have new parameters.

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