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Cryptography and Communications

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15-07-2020

Two constructions of asymptotically optimal codebooks via the trace functions

Authors: Xia Wu, Wei Lu, Xiwang Cao

Published in: Cryptography and Communications | Issue 6/2020

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Abstract

In this paper, we present two new constructions of complex codebooks with multiplicative characters, additive characters and trace functions over finite fields, and determin 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, in the first construction, we generalize the result in Zhang and Feng (IEEE Trans. Inform. Theory 58(4), 2507–2511, 2012). In the second construction, we generalize the results in Hong et al. (IEEE Trans. Inf. Theory 60(6), 3698–3705, 2014), we can asymptotically achieve Welch bound for any odd prime p, we also derive the whole distribution of their inner products. The parameters of these codebooks are new.

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Title: Two constructions of asymptotically optimal codebooks via the trace functions
Authors: Xia Wu
Wei Lu
Xiwang Cao
Publication date: 15-07-2020
Publisher: Springer US
Published in: Cryptography and Communications / Issue 6/2020
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-020-00448-w

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