Matrix groups related to the quaternion group and spherical orbit codes

Designs, Codes, and Cryptography

Volumn 37, Issue 3, 2005, Pages 391-404

  Dorofeev, A Ya ^a   Kazarin, L S ^a   Sidelnikov, V M ^a   Tuzhilin, M E ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b NONE

Author keywords

Finite group; Quaternion group; Spherical code; Spherical design

Indexed keywords

CODES (STANDARDS); MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA;

FINITE GROUP; QUATERNION GROUP; SPHERICAL CODE;

CRYPTOGRAPHY;

EID: 27244431757     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-004-4032-y     Document Type: Article

References (15)

1. V. M. Sidel'nikov, On a certain matrix group and codes on the Euclidean sphere, Problemy Peredachi Informacii, Vol. 33, No. 1 (1997) pp. 35-54;
2. English transl. in Problems Inform. Transmission Vol. 33, No. 1 (1997).
3. L. S. Kazarin, On the groups proposed by Sidel'nikov, Sbornik, Mathematics, Vol. 189, No. 7 (1998) pp. 1087-1100.
4. G. Nebe, E. M. Rains and N. J. A. Sloane, The invariants of the Clifford groups, preprint, Lehrstuhl B für Mathmatik, RWTH Aachen, (1999).
5. A. E. Zalesskii, Linear groups, Algebra-4, Sovrem. Problems in Matemat. Fund. Naprav, Vol. 37, M. (1989) pp. 114-228 (in Russian).
6. D. A. Suprunenko, Matrix Groups, M, Nauka (1972).
7. C. W. Curtis, W. M. Kantor and G. Seitz, The 2-transitive permutation representations of the finite Chevalley groups, Transactions of the American Mathematical Society Vol. 218 (1976) pp. 1-59.
8. M. Hall, The Theory of Groups, MacMillan, New York (1959).
9. V.D. Mazurov, The recognition of finite groups by the set of orders of its elements, Algebra and Logic, Vol. 37, No. 6 (1998) pp. 651-666 (in Russian).
10. V. Sidelnikov, New bounds for density of sphere packing in a n-dimensional Euclidean space, Mat. Sbornik, 93, 1(9), (1974)
11. =Math. USSR Sbornik Vol. 24 (1974) pp. 147-157.
12. P. Delsarte, J. M.Goethals and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata, Vol. 6 (1977) pp. 263-288.
13. J. M. Goethals and J. J. Seidel, Cubature formulae, polytopes, and spherical designs, in C. Devis, B. Grunbaum and F.A. Sherk, (eds.), Geometric Vein Springer-Verlag, Berlin (1981) pp. 203-218.
14. V. M. Sidelnikov, Orbital spherical 11-designs whose initial point is a root of an invariant polynomials. St. Peterburg Mathematical Journal, Vol. 11, No. 4, (2000) pp. 673-686.
15. T. Ericson and V. A. Zinoviev, Codes on Euclidean Sphere, Elsevier (2001).