I am in the middle of preparing a seminar lecture about spherical codes and as the source literature, I started reading “Codes on Euclidean Spheres” by Thomas Ericson and Victor Zinoviev. I really like the subject which leads to this question:

I am looking for application of spherical codes outside of data transmission. Ericson and Zinoviev mentioned in the introduction that Spherical codes have many applications in physics or biology. Other papers support this claim.
But at this moment I only have found a dissertation which has a chapter about their application in Quantum cryptography. As you can see, I am very interested to find more of their application, but I cannot find any.

I hope there might be some people at Mathematics who may know a few papers/articles about applications of spherical codes.

I am very grateful for any help.

Thanks, Hypertrooper

  • $\begingroup$ I'm not sure, but did you check whether Conway&Sloane has anything? I'm afraid I only know of the uses of spherical codes/designs in math and telecommunications. $\endgroup$ – Jyrki Lahtonen Jun 3 '17 at 6:03

The thesis by C. Torezzan cites the following references for applications of spherical codes:

Signal transmission:

  • Hamkins, J., & Zeger, K. Gaussian source coding with spherical codes. IEEE Trans. Inform. Theory 48, 11 (Nov. 2002), 2980–2989.
  • Karlof, J. Decoding spherical codes for the gaussian channel. IEEE Trans. Inform. Theory 39, 1 (1993), 60–65.

Spherical quantisation:

  • Hamkins, J., & Zeger, K. Optimal rate allocation for shape-gain gaussian quanti- zers. In Proc. IEEE International Symposium on Information Theory (24–29 June 2001), p. 182.

Numerical evaluation of integrals over spheres:

  • McLaren, A. D. Optimal numerical integration on a sphere. Math. Comp. 17 (1963), 361–383.

Applications in Chemistry:

  • Melnyk, T. W., Knop, O., & Smith, W. R. Extremal arrangements of points and unit charges on a sphere: equilibrium congurations revisited. Can. J. Chem. 55 (1977), 1745–1761.

Applications in Architecture and observations in nature:

  • Tarnay, T., & Gáspár, Z. Spherical circle-packing in nature, pratice and theory. Topologie Structurale 9 (1984), 39–58.

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