Quadratic Residues

  • Manfred R. Schroeder
Part of the Springer Series in Information Sciences book series (SSINF, volume 7)


Here we will acquaint ourselves with the fundamentals of quadratic residues and some of their applications, and learn how to solve quadratic congruences (or perhaps see when there is no solution).


Discrete Fourier Transform Primitive Root Quadratic Residue Legendre Symbol Concert Hall 
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  1. 15.1
    G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers, 5th ed., Sect. 6.5–7 ( Clarendon, Oxford 1984 )Google Scholar
  2. 15.2
    E. Jahnke, R. Emde: Tables of Functions ( Dover, New York 1945 )MATHGoogle Scholar
  3. 15.3
    M. Born, E. Wolf: Principles of Optics ( Pergamon, Oxford 1970 )Google Scholar
  4. 15.4
    M. R. Schroeder, R. E. Gerlach, A. Steingrube, H. W. Strube: Response to “Theory of Optimal Plane Diffusors. ” J. Acoust. Soc. Am. 66, 1647–1652 (1979)ADSCrossRefGoogle Scholar
  5. 15.5
    M. R. Schroeder: Constant-amplitude antenna arrays with beam patterns whose lobes have equal magnitudes. Archiv für Elektronik und Ubertragungstechnik (Electronics and Communication) 34, 165–168 (1980)Google Scholar
  6. 15.6
    J. E. Mazo: Some theoretical observations on spread-spectrum communications. Bell Syst. Tech. J. 58, 2013–2023 (1979)MathSciNetGoogle Scholar
  7. 15.7
    I. F. Blake, J. W. Mark: A note on complex sequences with low correlations. IEEE Trans. IT-28, 814–816 (1982)Google Scholar
  8. 15.8
    R. A. Scholtz: The origins of spread-spectrum communication. IEEE Trans. Communications, 30, 822–852 (1982); see also other articles in the same issue (May 1982)Google Scholar
  9. 15.9
    R. M. Lerner: Signals having good Correlation Functions. Western Electronic Show and Convention, San Francisco, August 1961. Paper 9/3Google Scholar
  10. 15.10
    S. W. Colomb: Shift Register Sequences ( Holden-Day, San Francisco 1967 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenFed. Rep. of Germany
  2. 2.Acoustics Speech and Mechanics ResearchBell LaboratoriesMurray HillUSA

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