### Abstract

Original language | English |
---|---|

Title of host publication | Sequences and Their Applications - SETA 2012 |

Editors | Tor Helleseth, Jonathan Jedwab |

Place of Publication | New York USA |

Publisher | Springer |

Pages | 159 - 167 |

Number of pages | 9 |

ISBN (Print) | 9783642306143 |

DOIs | |

Publication status | Published - 2012 |

Event | International Conference on Sequences and their Applications, 2012 - Waterloo, Canada Duration: 1 Jan 2012 → … |

### Conference

Conference | International Conference on Sequences and their Applications, 2012 |
---|---|

Country | Canada |

City | Waterloo |

Period | 1/01/12 → … |

### Cite this

*Sequences and Their Applications - SETA 2012*(pp. 159 - 167). New York USA: Springer. https://doi.org/10.1007/978-3-642-30615-0_15

}

*Sequences and Their Applications - SETA 2012.*Springer, New York USA, pp. 159 - 167, International Conference on Sequences and their Applications, 2012, Waterloo, Canada, 1/01/12. https://doi.org/10.1007/978-3-642-30615-0_15

**Perfect sequences of unbounded lengths over the basic quaternions.** / Barrera Acevedo, Santiago; Hall, Thomas Eric.

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

TY - GEN

T1 - Perfect sequences of unbounded lengths over the basic quaternions

AU - Barrera Acevedo, Santiago

AU - Hall, Thomas Eric

PY - 2012

Y1 - 2012

N2 - In this paper we show the existence of perfect sequences, of unbounded lengths, over the basic quaternions 1, -1,i, -i,j, -j,k, -k . Perfect sequences over the quaternion algebra were first introduced in 2009. One year later, a perfect sequence of length 5,354,228,880, over a quaternion alphabet with 24 elements, was shown. At this point two main questions were stated: Are there perfect sequences of unbounded lengths over the quaternion algebra? If so, is it possible to restrict the alphabet size to a small one? We answer these two questions by proving that any Lee sequence can always be converted into a sequence over the basic quaternions, which is an alphabet with 8 elements, and then by using the existence of Lee sequences of unbounded lengths to prove the existence of perfect sequences of unbounded lengths over the basic quaternions.

AB - In this paper we show the existence of perfect sequences, of unbounded lengths, over the basic quaternions 1, -1,i, -i,j, -j,k, -k . Perfect sequences over the quaternion algebra were first introduced in 2009. One year later, a perfect sequence of length 5,354,228,880, over a quaternion alphabet with 24 elements, was shown. At this point two main questions were stated: Are there perfect sequences of unbounded lengths over the quaternion algebra? If so, is it possible to restrict the alphabet size to a small one? We answer these two questions by proving that any Lee sequence can always be converted into a sequence over the basic quaternions, which is an alphabet with 8 elements, and then by using the existence of Lee sequences of unbounded lengths to prove the existence of perfect sequences of unbounded lengths over the basic quaternions.

UR - http://link.springer.com/chapter/10.1007%2F978-3-642-30615-0_15

U2 - 10.1007/978-3-642-30615-0_15

DO - 10.1007/978-3-642-30615-0_15

M3 - Conference Paper

SN - 9783642306143

SP - 159

EP - 167

BT - Sequences and Their Applications - SETA 2012

A2 - Helleseth, Tor

A2 - Jedwab, Jonathan

PB - Springer

CY - New York USA

ER -