We explore a notion of bent sequence attached to the data consisting of an Hadamard matrix of order $n$ defined over the complex $q^{th}$ roots of unity, an eigenvalue of that matrix, and a Galois automorphism from the cyclotomic field of order $q.$ In particular we construct self-dual bent sequences for various $q\le 60$ and lengths $n\le 21.$ Computational construction methods comprise the resolution of polynomial systems by Groebner bases and eigenspace computations. Infinite families can be constructed from regular Hadamard matrices, Bush-type Hadamard matrices, and generalized Boolean bent functions.As an application, we estimate the covering radius of the code attached to that matrix over $\Z_q.$ We derive a lower bound on that quantity for the Chinese Euclidean metric when bent sequences exist. We give the Euclidean distance spectrum, and bound above the covering radius of an attached spherical code, depending on its strength as a spherical design.

翻译：我们探索了一种与数据相关的bent序列概念，该数据由定义在复数$q$次单位根上的$n$阶Hadamard矩阵、该矩阵的一个特征值以及来自$q$次分圆域的伽罗瓦自同构构成。特别地，针对$q\le 60$和长度$n\le 21$的各种情形，我们构造了自对偶bent序列。计算构造方法包括通过Gröbner基求解多项式系统以及特征空间计算。无穷族可由正则Hadamard矩阵、Bush型Hadamard矩阵和广义布尔bent函数构造。作为应用，我们估计了该矩阵所关联的$\Z_q$码的覆盖半径。当bent序列存在时，我们给出了该量在Chinese Euclidean度量下的下界。我们给出了欧氏距离谱，并基于其作为球面设计的强度，给出了关联球面码覆盖半径的上界。