A note on classification of binary signal set in the view of Hadamard equivalence

• Published in: 2009 Fourth International Workshop on Signal Design and its Applications in Communications pp. 100 - 103
• Main Authors: Ki-Hyeon Park, Hong-Yeop Song
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-10-2009
• Subjects: Algorithm design and analysis; Binary Signal Set; Chromium; Electronic mail; Error correction; Error correction codes; Hadamard Equivalence; Minimal Matrix
• ISBN: 1424443784; 9781424443796; 9781424443789; 1424443792
• ISSN: 2150-3680
• DOI: 10.1109/IWSDA.2009.5346402

In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. We propose a fast algorithm for checking the Hadamard equivalence for general binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to binary matrices of smaller sizes, and show the results. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size m times n, and show the solutions for small sizes, leaving many of the observed properties as open problems.