Abstract
We show that a p-ary polyphase sequence of period p2 from the Fermat quotients is 'perfect.' That is, its periodic autocorrelation is zero for all non-trivial shifts. We call this Fermat-Quotient sequences. Using this and the fact that the Frank-Zadoff sequences (which is known to be also perfect), we propose a collection of 'optimum' families of perfect polyphase sequences in the sense of Sarwate Bound. That is, the cross-correlation of two members in a family is upper bounded by p. We may say these families are 'completely optimum' since the cross-correlation of any two members in a family is exactly p for all phase-shifts.
Original language | English |
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Title of host publication | Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 1537-1540 |
Number of pages | 4 |
ISBN (Electronic) | 9781467377041 |
DOIs | |
Publication status | Published - 2015 Sep 28 |
Event | IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: 2015 Jun 14 → 2015 Jun 19 |
Publication series
Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2015-June |
ISSN (Print) | 2157-8095 |
Other
Other | IEEE International Symposium on Information Theory, ISIT 2015 |
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Country | Hong Kong |
City | Hong Kong |
Period | 15/6/14 → 15/6/19 |
Bibliographical note
Publisher Copyright:© 2015 IEEE.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics