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Finite field constructions of combinatorial arrays

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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.

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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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Authors and Affiliations

  1. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, K1K 6N5, Canada

    Lucia Moura

  2. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Gary L. Mullen

  3. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Daniel Panario

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  1. Lucia Moura
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  2. Gary L. Mullen
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  3. Daniel Panario
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Correspondence to Daniel Panario.

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This is one of several papers published in Designs, Codes and Cryptography comprising the 25th Anniversary Issue.

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Moura, L., Mullen, G.L. & Panario, D. Finite field constructions of combinatorial arrays. Des. Codes Cryptogr. 78, 197–219 (2016). https://doi.org/10.1007/s10623-015-0152-9

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