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Perfect root-of-unity codes with prime-size alphabetPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2011 (English)In: ICASSP2011, the 36th International Conference on Acoustics, Speech and Signal Processing, Prague, Czech Republic, 2011, 3136-3139- p.Conference paper (Refereed)
##### Abstract [en]

##### 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: 978-1-4577-0539-7OAI: 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
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2012-01-08 Created: 2012-01-08 Last updated: 2012-01-13Bibliographically approved

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.

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