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New nonexistence results on circulant weighing matrices

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Abstract

A weighing matrix W = (wi,j) is a square matrix of order n and entries wi,j in {0,± 1} such that WWT = kIn. In his thesis, Strassler gave a table of existence results for circulant weighing matrices with n ≤ 200 and k ≤ 100. In the latest version of Strassler’s table given by Tan, there are 34 open cases remaining. In this paper we give nonexistence proofs for 12 of these cases, report on preliminary searches outside Strassler’s table, and characterize the known proper circulant weighing matrices.

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Authors and Affiliations

  1. Riverside Research, 2640 Hibiscus Way, Beavercreek, OH, 45431, USA

    K. T. Arasu

  2. Center for Communications Research, 4320 Westerra Court, San Diego, CA, 92121, USA

    Daniel M. Gordon

  3. Loyola University, Chicago, IL, 60660, USA

    Yiran Zhang

Authors
  1. K. T. Arasu
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  2. Daniel M. Gordon
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  3. Yiran Zhang
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Correspondence to Daniel M. Gordon.

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REU research supported by an NSF grant, and presented at the Young Mathematicians’ Conference at OSU August 2015

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Arasu, K.T., Gordon, D.M. & Zhang, Y. New nonexistence results on circulant weighing matrices. Cryptogr. Commun. 13, 775–789 (2021). https://doi.org/10.1007/s12095-021-00492-0

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  • DOI: https://doi.org/10.1007/s12095-021-00492-0

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