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Open AccessArticle

Four Constructions of Asymptotically Optimal Codebooks via Additive Characters and Multiplicative Characters

by Xia Wu and Wei Lu *
School of Mathematics, Southeast University, Nanjing 210096, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1144; https://doi.org/10.3390/math7121144
Received: 23 September 2019 / Revised: 5 November 2019 / Accepted: 19 November 2019 / Published: 23 November 2019
(This article belongs to the Special Issue Information Theory, Cryptography, Randomness and Statistical Modeling)
In this paper, we present four new constructions of complex codebooks with multiplicative characters, additive characters, and quadratic irreducible polynomials and determine the maximal cross-correlation amplitude of these codebooks. We prove that the codebooks we constructed are asymptotically optimal with respect to the Welch bound. Moreover, we generalize the result obtained by Zhang and Feng and contain theirs as a special case. The parameters of these codebooks are new. View Full-Text
Keywords: codebook; asymptotic optimality; Welch bound; Gauss sum; Jacobi sum codebook; asymptotic optimality; Welch bound; Gauss sum; Jacobi sum
MDPI and ACS Style

Wu, X.; Lu, W. Four Constructions of Asymptotically Optimal Codebooks via Additive Characters and Multiplicative Characters. Mathematics 2019, 7, 1144.

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