Designs, Codes and Cryptography

, Volume 64, Issue 1, pp 143-151

First online:

New restrictions on possible orders of circulant Hadamard matrices

  • Ka Hin LeungAffiliated withDepartment of Mathematics, National University of Singapore
  • , Bernhard SchmidtAffiliated withDivision of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University Email author 

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We obtain several new number theoretic results which improve the field descent method. We use these results to rule out many of the known open cases of the circulant Hadamard matrix conjecture. In particular, the only known open case of the Barker sequence conjecture is settled.


Circulant Hadamard matrices Barker sequences Field descent

Mathematics Subject Classification (2000)

15B34 05B10