, Volume 64, Issue 1-2, pp 143-151
Date: 13 Mar 2011

New restrictions on possible orders of circulant Hadamard matrices

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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.

This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Geometry, Combinatorial Designs & Cryptology”.