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Multilevel and multidimensional Hadamard matrices

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Abstract

Multilevel Hadamard matrices (MHMs), whose entries are integers as opposed to the traditional restriction to {±1}, were introduced by Trinh, Fan, and Gabidulin in 2006 as a way to construct multilevel zero-correlation zone sequences, which have been studied for use in approximately synchronized code division multiple access systems. We answer the open question concerning the maximum number of distinct elements permissible in an order n MHM by proving the existence of an order n MHM with n elements of distinct absolute value for all n. We also define multidimensional MHMs and prove an analogous existence result.

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Authors and Affiliations

  1. Franklin W. Olin College of Engineering, Needham, MA, USA

    Sarah Spence Adams, Matthew Crawford, Caitlin Greeley & Bryce Lee

  2. Indian Institute of Technology, Kharagpur, India

    Mathav Kishore Murugan

Authors
  1. Sarah Spence Adams
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  2. Matthew Crawford
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  3. Caitlin Greeley
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  4. Bryce Lee
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  5. Mathav Kishore Murugan
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Corresponding author

Correspondence to Sarah Spence Adams.

Additional information

Communicated by K. T. Arasu.

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Adams, S.S., Crawford, M., Greeley, C. et al. Multilevel and multidimensional Hadamard matrices. Des. Codes Cryptogr. 51, 245–252 (2009). https://doi.org/10.1007/s10623-008-9258-7

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  • DOI: https://doi.org/10.1007/s10623-008-9258-7

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