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Non-existence of Some Nearly Perfect Sequences, Near Butson–Hadamard Matrices, and Near Conference Matrices
Date
2018-09-01
Author
Winterhof, Arne
Yayla, Oğuz
Ziegler, Volker
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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. We refine the idea of Brock on the unsolvability of certain equations in the case of cyclotomic number fields whose ring of integers is not a principal ideal domain and get many new non-existence results for near BH matrices and near conference matrices. We also apply previous results on vanishing sums of roots of unity and self conjugacy condition to derive non-existence results for near BH matrices and near conference matrices.
URI
https://hdl.handle.net/11511/69080
Journal
Mathematics in Computer Science
DOI
https://doi.org/10.1007/s11786-018-0383-z
Collections
Graduate School of Applied Mathematics, Article
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A. Winterhof, O. Yayla, and V. Ziegler, “Non-existence of Some Nearly Perfect Sequences, Near Butson–Hadamard Matrices, and Near Conference Matrices,”
Mathematics in Computer Science
, pp. 465–471, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69080.