Abstract
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.
| Original language | English |
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| 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: 4 Jun 2012 → 8 Jun 2012 Conference number: 7th https://link.springer.com/book/10.1007/978-3-642-30615-0 (Proceedings) |
Conference
| Conference | International Conference on Sequences and their Applications 2012 |
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| Abbreviated title | SETA 2012 |
| Country/Territory | Canada |
| City | Waterloo |
| Period | 4/06/12 → 8/06/12 |
| Internet address |
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