Designs, Codes and Cryptography

, Volume 78, Issue 1, pp 197–219 | Cite as

Finite field constructions of combinatorial arrays

Article
First Online:
Accepted:

Abstract

We survey a number of topics and constructions of combinatorial arrays based on finite fields. These combinatorial objects include orthogonal arrays, covering arrays, ordered orthogonal arrays, permutation arrays, frequency permutation arrays, hypercubes and Costas arrays.

Keywords

Orthogonal array Covering array Permutation array Frequency permutation array Hypercubes Costas arrays 

Mathematics Subject Classification

05BXX 11TXX 94A55 
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Notes

Acknowledgments

We would like to thank Dieter Jungnickel, Brett Stevens, David Thomson and Peter Wild for many valuable suggestions that improved this manuscript.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceUniversity of OttawaOttawaCanada
  2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA
  3. 3.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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