### Abstract

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 x n, and show the solutions for small sizes, leaving many of the observed properties as open problems.

Original language | English |
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Title of host publication | Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09 |

Pages | 100-103 |

Number of pages | 4 |

DOIs | |

Publication status | Published - 2009 |

Event | 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09 - Fukuoka, Japan Duration: 2009 Oct 19 → 2009 Oct 23 |

### Publication series

Name | Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09 |
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### Other

Other | 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09 |
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Country | Japan |

City | Fukuoka |

Period | 09/10/19 → 09/10/23 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Signal Processing
- Electrical and Electronic Engineering
- Communication

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## Cite this

*Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09*(pp. 100-103). [5346402] (Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09). https://doi.org/10.1109/IWSDA.2009.5346402