Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Cryptography and Communications
Erschienen in: Cryptography and Communications 1/2014

01.03.2014

A complementary construction using mutually unbiased bases

verfasst von: Gaofei Wu, Matthew Geoffrey Parker

Erschienen in: Cryptography and Communications | Ausgabe 1/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We propose a construction for complementary sets of arrays that exploits a set of mutually-unbiased bases (a MUB). In particular we present, in detail, the construction for complementary pairs that is seeded by a MUB of dimension 2, where we enumerate the arrays and the corresponding set of complementary sequences obtained from the arrays by projection. We also sketch an algorithm to uniquely generate these sequences. The pairwise squared inner-product of members of the sequence set is shown to be \(\frac {1}{2}\). Moreover, a subset of the set can be viewed as a codebook that asymptotically achieves \(\sqrt {\frac {3}{2}}\) times the Welch bound.
Vorheriger Artikel Special issue editorial: Sequences and their applications
Nächster Artikel A simple suboptimal construction of cross-bifix-free codes

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
Up to trivial symmetries and, for a fixed δ, there may be more than one choice of ℳ δ .
 
2
Comparing \(F_{k}(z)F_{k}^{*}\left (z^{-1}\right )\) with F † z − 1 F(z), we see that, whilst z − 1 is on the right for the former it is on the left for the latter. This is simply because F is a S × 1 vector - there is no deeper meaning.
 
3
More accurately, we should write f k (π(x)) to indicate one of 6 possible permutations but, to reduce notation, we make such a mapping implicit in this paper.
 
Literatur
1.
Barthelemy, J.P: An asymptotic equivalent for the number of total preorders on a finite set. Discret. Math. 29(3), 311–313 (1980)CrossRefMATHMathSciNet
2.
Bian, X., Yu, N.Y: Partial fourier codebooks associated with multiplied golay complementary sequences for compressed sensing. Sequences and Their Applications - SETA 2012 Lecture Notes in Computer Science, vol. 7280, pp. 257–268, 2012
3.
Bjørstad, T.E., Parker, M.G.: Equivalence between certain complementary pairs of types I and III. In: Preneel, B., Dodunekov, S., Rijmen, V., Nikova, S. (eds.) Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes. Invited talk at NATO Science for Peace and Security Series - D: Information and Communication Security, vol. 23. http://​www.​ii.​uib.​no/​matthew/​CompEquivCorrect​ed.​ pdf (2009)
4.
Budǐsin, S.Z.: New complementary pairs of sequences. Electron. Lett. 26, 881–883 (1990)CrossRef
5.
Budǐsin, S.Z., Spasojević, P.: Filter bank representation of complementary sequence pairs. In: 15th Annual Allerton Conference. Allerton House, UIUC, Illinois (2012)
6.
Budǐsin, S.Z., Spasojević, P.: Paraunitary generation/correlation of QAM complementary sequence pairs. Crypt. Commun. 5(3) (2013)
7.
8.
Davis, J.A., Jedwab, J.: Peak-to-mean power control for OFDM, Golay complementary sequences, and Reed-Muller codes. IEEE Trans. Inform. Theory 45(11), 2397–2417 (1999)CrossRefMATHMathSciNet
9.
Durt, T., Englert, B.-G., Bengtsson, I., Zyczkowski, K.: On mutually unbiased bases. Int. J. Quantum Inf. 8, 535–640 (2010). arXiv:1004.​3348 [quant-ph]CrossRefMATH
10.
Fiedler, F., Jedwab, J., Parker, M.G.: A multi-dimensional approach to the construction and enumeration of Golay complementary sequences. J. Comb. Theory (Series A) 115, 753–776 (2008)CrossRefMATHMathSciNet
11.
Fiedler, F., Jedwab, J., Parker, M.G.: A framework for the construction of Golay sequences. IEEE Trans. Inform. Theory 54(7), 3113–3129 (2008)CrossRefMathSciNet
12.
13.
Hein, M., Dur, W., Eisert, J., Raussendorf, R., Van den Nest, M., Briegel, H.-J.: Entanglement in graph states and its applications. In: Zoller, P., Casati, G., Shepelyansky, D., Benenti, G. (eds.) International School of Physics Enrico Fermi (Varenna, Italy), Quantum Computers, Algorithms and Chaos, vol. 162. arXiv:0602096 [quant-ph] (2006)
14.
Ivanović, I.D.: Geometrical description of quantal state determination. J. Phys. A 14(12), 3241–3245 (1981)CrossRefMathSciNet
15.
16.
Kschischang, F.R., Frey, B.J., Loeliger, H.-A.: Factor graphs and the sum-product algorithm. IEEE Trans. Inform. Theory 47(2) (2001)
17.
Matsufuji, S., Shigemitsu, R., Tanada, Y., Kuroyanagi, N.: Construction of complementary arrays. In: Proceedings of Sympotic’04, pp. 78–81 (2004)
18.
19.
Parker, M.G., Tellambura, C.: Golay-Davis-Jedwab complementary sequences and rudin-shapiro constructions. In:International Symposium in Information Theory, p. 302. Sorrento (2000)
20.
21.
Parker, M.G., Riera, C.: Generalised complementary arrays. Lecture Notes in Computer Science, LNCS, vol. 7089. Springer (2011)
22.
Paterson, K.G.: Generalized Reed-Muller codes and power control in OFDM modulation. IEEE Trans. Inform. Theory 46, 104–120 (2000)CrossRefMATHMathSciNet
23.
24.
Ruskai, M.B.: Some connections between frames, mutually unbiased bases, and POVM’s in quantum information theory. Acta Appl. Math. 108(3), 709–719 (2009)CrossRefMATHMathSciNet
25.
Sarwate, D.: Meeting the Welch bound with equality. In: Proceedings of SETA’98 Sequences Their Application, pp. 79–102. Springer, London (1999)CrossRef
26.
Schmidt, K.-U.: On cosets of the generalized first-order Reed-Muller code with low PMEPR. IEEE Trans. Inf. Theory 52(7), 3220–3232 (2006)CrossRef
27.
Schmidt, K.-U.: Complementary sets, generalized Reed-Muller codes, and power control for OFDM. IEEE Trans. Inf. Theory 53(2), 808–814 (2007)CrossRef
28.
Schwinger, J.: Unitary Operator Bases. Harvard University (1960)
29.
Shapiro, H.S.: Extremal Problems for Polynomials and Power Series. Master’s thesis, Mass. Inst. of Technology (1951)
30.
Suehiro, N., Hatori, M.: N-shift cross-orthogonal sequences. IEEE Trans. Inform. Theory IT-34(1), 143–146 (1988)CrossRefMathSciNet
31.
Wang, Z., Parker, M.G., Gong, G., Wu, G.: On the PMEPR of binary Golay sequences of length 2 n . submitted (June 2013)
32.
33.
Wilf, H.S.: Generating Functionology, 2nd edn. Academic, NY (1994)
Metadaten
Titel
A complementary construction using mutually unbiased bases
verfasst von
Gaofei Wu
Matthew Geoffrey Parker
Publikationsdatum
01.03.2014
Verlag
Springer US
Erschienen in
Cryptography and Communications / Ausgabe 1/2014
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-013-0095-9

Weitere Artikel der Ausgabe 1/2014

Cryptography and Communications 1/2014 Zur Ausgabe

OriginalPaper

A simple suboptimal construction of cross-bifix-free codes

OriginalPaper

Paraunitary generation/correlation of QAM complementary sequence pairs

OriginalPaper

Perfect arrays of unbounded sizes over the basic quaternions

EditorialNotes

Special issue editorial: Sequences and their applications

ReviewPaper

New near perfect sequences of even lengths