### Abstract

Original language | English |
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Title of host publication | Signal Design and its Applications in Communications |

Editors | Pingzhi Fan, Naoki Suehiro |

Place of Publication | Fukuoka Japan |

Publisher | IEEE, Institute of Electrical and Electronics Engineers |

Pages | 8 - 11 |

Number of pages | 4 |

ISBN (Print) | 9781424443796 |

Publication status | Published - 2009 |

Event | International Workshop on Signal Design and its Applications in Communications (IWSDA) 2009 - Fukuoka Japan, Fukuoka Japan Duration: 1 Jan 2009 → … |

### Conference

Conference | International Workshop on Signal Design and its Applications in Communications (IWSDA) 2009 |
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City | Fukuoka Japan |

Period | 1/01/09 → … |

### Cite this

*Signal Design and its Applications in Communications*(pp. 8 - 11). Fukuoka Japan: IEEE, Institute of Electrical and Electronics Engineers.

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*Signal Design and its Applications in Communications.*IEEE, Institute of Electrical and Electronics Engineers, Fukuoka Japan, pp. 8 - 11, International Workshop on Signal Design and its Applications in Communications (IWSDA) 2009, Fukuoka Japan, 1/01/09.

**Perfect sequences over the real quaternions.** / Kuznetsov, Oleg.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - Perfect sequences over the real quaternions

AU - Kuznetsov, Oleg

PY - 2009

Y1 - 2009

N2 - Abstract In this paper, perfect sequences over real quaternions are considered. Definitions for the right and left periodic autocorrelation functions are given, and right and left perfect sequences introduced. It is shown that the right (left) perfection of any sequence implies the left (right) perfection, so concepts of right and left perfect sequences over the real quaternions are equivalent. Unitary transformations of the quaternion space H are then considered. Using the equivalence of the right and left perfection, it is proved that unitary transformations of the quaternion space `respect perfection of a sequence. Consequently, any symmetry transformation of the alphabet preserves perfection of a sequence.

AB - Abstract In this paper, perfect sequences over real quaternions are considered. Definitions for the right and left periodic autocorrelation functions are given, and right and left perfect sequences introduced. It is shown that the right (left) perfection of any sequence implies the left (right) perfection, so concepts of right and left perfect sequences over the real quaternions are equivalent. Unitary transformations of the quaternion space H are then considered. Using the equivalence of the right and left perfection, it is proved that unitary transformations of the quaternion space `respect perfection of a sequence. Consequently, any symmetry transformation of the alphabet preserves perfection of a sequence.

UR - http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5346443

M3 - Conference Paper

SN - 9781424443796

SP - 8

EP - 11

BT - Signal Design and its Applications in Communications

A2 - Fan, Pingzhi

A2 - Suehiro, Naoki

PB - IEEE, Institute of Electrical and Electronics Engineers

CY - Fukuoka Japan

ER -