Six constructions of asymptotically optimal codebooks via the character sums

@article{Lu2019SixCO,
  title={Six constructions of asymptotically optimal codebooks via the character sums},
  author={Wenlong Lu and Xia Wu and Xiwang Cao and Ming Chen},
  journal={Designs, Codes and Cryptography},
  year={2019},
  volume={88},
  pages={1139-1158}
}
  • W. LuXia Wu Ming Chen
  • Published 1 November 2019
  • Computer Science, Mathematics
  • Designs, Codes and Cryptography
In this paper, using additive characters of finite field, we find a codebook which is equivalent to the measurement matrix in Mohades et al. (IEEE Signal Process Lett 21(7):839–843, 2014). The advantage of our construction is that it can be generalized naturally to construct the other five classes of codebooks using additive and multiplicative characters of finite field. We determine the maximum cross-correlation amplitude of these codebooks by the properties of characters and character sums… 
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11 Citations

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References

SHOWING 1-10 OF 33 REFERENCES

Two constructions of asymptotically optimal codebooks via the trace functions

It is proved that the codebooks constructed are asymptotically optimal with respect to the Welch bound, and the maximal cross-correlation amplitude of these codebooks is determined.

Constructions of Codebooks Asymptotically Achieving the Welch Bound With Additive Characters

Following the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are obtained and the resulting codebooks could have a small alphabet size.

Two Constructions of Asymptotically Optimal Codebooks via the Hyper Eisenstein Sum

A new character sum, the hyper Eisenstein sum, is presented and the properties of this character sum are studied and the codebooks generated by these constructions asymptotically meet the Welch bound.

New Constructions of Asymptotically Optimal Codebooks With Multiplicative Characters

In this paper, two new constructions of infinitely many codebooks with multiplicative characters of finite fields are presented, which produce complex codebooks asymptotically achieving the Levenshtein bound and code books asymptic achieving the Welch bound.

Nearly optimal codebooks based on generalized Jacobi sums

New Constructions of Codebooks Nearly Meeting the Welch Bound With Equality

This paper proposes new constructions of codebooks nearly meeting the Welch bound with equality using difference sets and the product of Abelian groups, which yield many codebooks with new parameters.

New Constructions of Codebooks Asymptotically Achieving the Welch Bound

  • Gaojun LuoXiwang Cao
  • Computer Science, Mathematics
    2018 IEEE International Symposium on Information Theory (ISIT)
  • 2018
The complex codebooks produced by these two constructions are proved to be asymptotically optimal with respect to the Welch bound.

Achieving the Welch bound with difference sets

This work constructs analytically optimal codebooks meeting the Welch lower bound, and develops an efficient numerical search method based on a generalized Lloyd algorithm that leads to considerable improvement on the achieved I/sub max/ over existing alternatives.

Near-Optimal Partial Hadamard Codebook Construction Using Binary Sequences Obtained From Quadratic Residue Mapping

It is proved that the maximum magnitude of inner products between the code vectors of the proposed codebooks asymptotically achieves the Welch bound equality for sufficiently large p and derive their inner product distribution.

A Generic Construction of Complex Codebooks Meeting the Welch Bound

  • C. DingTao Feng
  • Computer Science
    IEEE Transactions on Information Theory
  • 2007
The objectives of this correspondence are to present a generic construction of MWBE codebooks that contains the previous two constructions as special cases and describe new MWBEcodebooks that cannot be produced by the earlier two construction.