Designs, Codes and Cryptography

, Volume 64, Issue 1, pp 143–151

New restrictions on possible orders of circulant Hadamard matrices

Authors

  • Ka Hin Leung
    • Department of MathematicsNational University of Singapore
    • Division of Mathematical Sciences, School of Physical & Mathematical SciencesNanyang Technological University
Article

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

Abstract

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.

Keywords

Circulant Hadamard matricesBarker sequencesField descent

Mathematics Subject Classification (2000)

15B3405B10

Copyright information

© Springer Science+Business Media, LLC 2011