一种基于超立方体图的Hadamard矩阵构造法

Constructions for Hadamard Matrices Based on Hypercube Graph

Hadamard矩阵是一种十分特殊的正交矩阵。它在区组设计、数据压缩、数字图象处理、数据挖掘、信息安全、通信理论、量子计算、编码理论等诸多领域有着广泛的应用。然而,Hadamard矩阵的构造问题至今仍是一个悬而未决的问题。本文针对该问题提出了一种新的Hadamard矩阵构造法,并通过具体实例展示了本文所提出的方法的可行性。

Hadamard matrices are a special type of orthogonal matrices. The applications of Hadamard matrices include combinatorial designs, data compression, digital image processing, data mining, information security, communication theory, quantum computing, coding theory, etc. However, construction problem for Hadamard matrices is remain unsolved. In this paper, we propose a novel construction method for Hadamard matrices. Using some illustrated examples, we conclude that our method is effective.