Designs, Codes and Cryptography

, Volume 64, Issue 1, pp 143–151

New restrictions on possible orders of circulant Hadamard matrices


DOI: 10.1007/s10623-011-9493-1

Cite this article as:
Leung, K.H. & Schmidt, B. Des. Codes Cryptogr. (2012) 64: 143. doi:10.1007/s10623-011-9493-1


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 matricesBarker sequencesField descent

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore
  2. 2.Division of Mathematical Sciences, School of Physical & Mathematical SciencesNanyang Technological UniversitySingaporeRepublic of Singapore