turkmath.org

In this talk, the unsolvability of certain equations $\alpha\overline{\alpha} = \omega$ over the ring of integers of cyclotomic number fields whose ring of integers is not a principal ideal domain will be presented. The method is a generalization of the idea of Brock. This method is used for the non-existence problem of (nearly) perfect (almost) m-ary sequences via their connection to (near) Butson-Hadamard (BH) matrices and (near) conference matrices. We show some new non-existence results for near BH matrices and near conference matrices. The previously known methods for deriving non-existence results will also be presented: vanishing sums of roots of unity and self conjugacy. We wil also mention the contribution of Akyildiz-Guloglu-Ikeda in this direction. This is a joint work with Arne Winterhof and Volker Ziegler.