Two constructions of asymptotically optimal codebooks via the trace functions

@article{Wu2019TwoCO,
  title={Two constructions of asymptotically optimal codebooks via the trace functions},
  author={Xia Wu and Wei Lu and Xiwang Cao and Ming Chen},
  journal={Cryptography and Communications},
  year={2019},
  volume={12},
  pages={1195 - 1211}
}
  • Xia WuW. Lu Ming Chen
  • Published 6 May 2019
  • Computer Science, Mathematics
  • Cryptography and Communications
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… 

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