### Abstract

In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. To do this, we study various properties of this equivalence relation and its classes. We propose to use a concept named "HR-minimal" as a representative of each equivalence class, and some properties and constructions of HR-minimals are investigated. Especially, careful observation about the weight on an HR-minimal's second row are performed since it is highly related with orthogonality of a matrix. We give a construction ensuring sufficiently large m at some condition. We also give an exhaustive search algorithm to find the maximum m at given n and second row weight. Moreover, HR-minimals with the largest weight on its second row, defined as Quasi-Hadamard matrices (QH matrices), are studied. They include Hadamard matrices as a special case and generalize the property of Hadamard matrices in the sense that the row vectors of m × n QH matrices form a set of m binary vectors of length n with minimum pairwise absolute correlation. Some properties and existence of QH matrices are also discussed, including the examples of 16 × (6, 10, 17) QH matrices found by computer.

Original language | English |
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Title of host publication | Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11 |

Pages | 60-63 |

Number of pages | 4 |

DOIs | |

Publication status | Published - 2011 Dec 1 |

Event | 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11 - Guilin, China Duration: 2011 Oct 10 → 2011 Oct 14 |

### Other

Other | 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11 |
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Country | China |

City | Guilin |

Period | 11/10/10 → 11/10/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Computer Science Applications
- Signal Processing

### Cite this

*Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11*(pp. 60-63). [6159441] https://doi.org/10.1109/IWSDA.2011.6159441

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*Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11.*, 6159441, pp. 60-63, 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11, Guilin, China, 11/10/10. https://doi.org/10.1109/IWSDA.2011.6159441

**Classification, construction and search of general quasi-orthogonal binary signal sets.** / Park, Ki Hyeon; Song, Hong Yeop.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Classification, construction and search of general quasi-orthogonal binary signal sets

AU - Park, Ki Hyeon

AU - Song, Hong Yeop

PY - 2011/12/1

Y1 - 2011/12/1

N2 - In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. To do this, we study various properties of this equivalence relation and its classes. We propose to use a concept named "HR-minimal" as a representative of each equivalence class, and some properties and constructions of HR-minimals are investigated. Especially, careful observation about the weight on an HR-minimal's second row are performed since it is highly related with orthogonality of a matrix. We give a construction ensuring sufficiently large m at some condition. We also give an exhaustive search algorithm to find the maximum m at given n and second row weight. Moreover, HR-minimals with the largest weight on its second row, defined as Quasi-Hadamard matrices (QH matrices), are studied. They include Hadamard matrices as a special case and generalize the property of Hadamard matrices in the sense that the row vectors of m × n QH matrices form a set of m binary vectors of length n with minimum pairwise absolute correlation. Some properties and existence of QH matrices are also discussed, including the examples of 16 × (6, 10, 17) QH matrices found by computer.

AB - In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. To do this, we study various properties of this equivalence relation and its classes. We propose to use a concept named "HR-minimal" as a representative of each equivalence class, and some properties and constructions of HR-minimals are investigated. Especially, careful observation about the weight on an HR-minimal's second row are performed since it is highly related with orthogonality of a matrix. We give a construction ensuring sufficiently large m at some condition. We also give an exhaustive search algorithm to find the maximum m at given n and second row weight. Moreover, HR-minimals with the largest weight on its second row, defined as Quasi-Hadamard matrices (QH matrices), are studied. They include Hadamard matrices as a special case and generalize the property of Hadamard matrices in the sense that the row vectors of m × n QH matrices form a set of m binary vectors of length n with minimum pairwise absolute correlation. Some properties and existence of QH matrices are also discussed, including the examples of 16 × (6, 10, 17) QH matrices found by computer.

UR - http://www.scopus.com/inward/record.url?scp=84858379753&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858379753&partnerID=8YFLogxK

U2 - 10.1109/IWSDA.2011.6159441

DO - 10.1109/IWSDA.2011.6159441

M3 - Conference contribution

AN - SCOPUS:84858379753

SN - 9781612840468

SP - 60

EP - 63

BT - Proceedings of the 5th International Workshop on Signal Design and Its Applications in Communications, IWSDA'11

ER -