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arXiv · 1407.6548

Non-Existence of Some Nearly Perfect Sequences, Near Butson-Hadamard Matrices, and Near Conference Matrices

Arne Winterhof·Oğuz Yayla·Volker Ziegler
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Abstract

In this paper we study the non-existence problem of (nearly) perfect (almost) $m$-ary sequences via their connection to (near) Butson-Hadamard (BH) matrices and (near) conference matrices. Firstly, we apply a result on vanishing sums of roots of unity and a result of Brock on the unsolvability of certain equations over a cyclotomic number field to derive non-existence results for near BH matrices and near conference matrices. Secondly, we refine the idea of Brock in the case of cyclotomic number fields whose ring of integers is not a principal ideal domains and get many new non-existence results.

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Arne Winterhof, Oğuz Yayla, Volker Ziegler. 2014-07-24. Non-Existence of Some Nearly Perfect Sequences, Near Butson-Hadamard Matrices, and Near Conference Matrices. https://arxiv.org/abs/1407.6548

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