近似完美序列、近似Butson-Hadamard矩阵和近似协商矩阵的不存在性
Non-Existence of Some Nearly Perfect Sequences, Near Butson-Hadamard Matrices, and Near Conference Matrices
摘要：
本文通过（近）Butson-Hadamard（BH）矩阵和（近）会议矩阵的关系，研究了（近）完美（近）$m$ -元序列的不存在性问题.首先，我们应用一个关于单位根消失和的结果和Brock关于分圆数域上某些方程的不可解性的结果，得到了近BH矩阵和近会议矩阵的不存在性结果。其次，在整数环不是主理想整环的分圆数域的情形下，我们改进了Brock的思想，得到了许多新的不存在性结果。
英文摘要：
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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