# American Institute of Mathematical Sciences

December  2020, 10(4): 571-578. doi: 10.3934/naco.2020052

## The research on the properties of Fourier matrix and bent function

 1 School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou, 215500, China 2 Shanghai Seed Power Enterprise Management Cosulting Co., LTD, Minhang District, Shanghai, 201200, China 3 Asset Management Department, Jiangsu Zijin Rural Commercial Bank Co., LTD, Nanjing, 210023, China

* Corresponding author: Li Zhang

Received  April 2020 Revised  September 2020 Published  September 2020

Fund Project: The first author is supported by NSF grant 10231060

This paper first gives out basic background and some definitions and propositions for Fourier matrix and bent function. Secondly we construct an standard orthogonal basis by the eigenvectors of the corresponding Fourier matrix. At last the diagonalization work of Fourier matrix is completed and some theorems about them are proved.

Citation: Li Zhang, Xiaofeng Zhou, Min Chen. The research on the properties of Fourier matrix and bent function. Numerical Algebra, Control & Optimization, 2020, 10 (4) : 571-578. doi: 10.3934/naco.2020052
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