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Perfect root-of-unity codes with prime-size alphabet
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2011 (English)In: ICASSP2011, the 36th International Conference on Acoustics, Speech and Signal Processing, Prague, Czech Republic, 2011, 3136-3139- p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, Perfect Root-of-Unity Codes (PRUCs) with entries in alpha(p) = {x is an element of C | x(p) = 1} where p is a prime are studied. A lower bound on the number of distinct phases in PRUCs over alpha(p) is derived. We show that PRUCs of length L >= p(p - 1) must use all phases in alpha(p). It is also shown that if there exists a PRUC of length L over alpha(p) then p divides L. We derive equations (which we call principal equations) that give possible lengths of a PRUC over alpha(p) together with their phase distribution. Using these equations, we prove for example that the length of a 3-phase perfect code must be of the form L = 1/4 (9h(1)(2) + 3h(2)(2)) for (h(1), h(2)) is an element of Z(2) and we also give the exact number of occurences of each element from alpha(3) in the code. Finally, all possible lengths (<= 100) of PRUCs over alpha(5) and alpha(7) together with their phase distributions are provided.

Place, publisher, year, edition, pages
2011. 3136-3139- p.
Series
International Conference on Acoustics Speech and Signal Processing ICASSP, ISSN 1520-6149
Keyword [en]
Perfect codes, Root-of-unity codes, Periodic autocorrelation, Phase distribution
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:uu:diva-165499ISI: 000296062403137ISBN: 978-1-4577-0539-7 (print)OAI: oai:DiVA.org:uu-165499DiVA: diva2:473993
Conference
IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) MAY 22-27, 2011 Prague, CZECH REPUBLIC
Available from: 2012-01-08 Created: 2012-01-08 Last updated: 2012-01-13Bibliographically approved

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Soltanalian, MojtabaStoica, Peter

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