# 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} }

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…

## 7 Citations

### Six constructions of asymptotically optimal codebooks via the character sums

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Using additive characters of finite field, this paper finds a codebook which is equivalent to the measurement matrix in Mohades et al. and proves that all the codebooks constructed are asymptotically optimal with respect to the Welch bound.

### Six constructions of asymptotically optimal codebooks via the character sums

- Computer Science, MathematicsDes. Codes Cryptogr.
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Using additive characters of finite field, this paper finds a codebook which is equivalent to the measurement matrix in Mohades et al. and proves that all the codebooks constructed are asymptotically optimal with respect to the Welch bound.

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

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Four new constructions of complex codebooks with multiplicative characters, additive characters, and quadratic irreducible polynomials are presented and it is proved that the codebooks constructed are asymptotically optimal with respect to the Welch bound.

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: In this paper, we present four new constructions of complex codebooks with multiplicative characters, additive characters, and quadratic irreducible polynomials and determine the maximal…

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The codebooks constructed in this paper are nearly optimal with respect to the Welch bound, and their parameters are new.

### A Complete Bibliography of Publications in Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences

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