Radon transforms and packings

Discrete Applied Mathematics

Volumn 111, Issue 1-2, 2001, Pages 3-22

  Boguslavsky, Michael I ^a  

^a INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035879622     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(00)00341-3     Document Type: Article

References (31)

1. Boguslavsky M. On the number of solutions of polynomial systems. Finite Fields Appl. 3:1997;287-299.
2. M. Boguslavsky, Lattices, codes, and Radon transforms, Ph.D. Thesis, Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1999.
3. M. Boguslavsky, Generalized Hermitian constants and kissing numbers, Proceedings of the Sixth International Workshop "Algebraic and Combinatorial Coding Theory", Pskov, Russia, September 1998, pp. 46-51.
4. M. Boguslavsky, Lattices, Codes, and Radon transforms, Proceedings of the Workshop on Coding and Cryptography'99, INRIA, Paris, February 1999.
5. Buser P., Sarnak P. On the period matrix of a Riemann surface of large genus. Invent. Math. 117(1):1994;27-56.
6. Conway J., Hardin R., Sloane N. Packing lines, planes, etc.: packings in Grassmannian spaces. Exp. Math. 5(2):1996;139-159.
7. Coulangeon R. Réseaux. k -extrêmes Proc. London Math. Soc. (3). 73(3):1996;555-574.
8. Coulangeon R. Minimal vectors in the second exterior power of a lattice. J. Algebra. 194(2):1997;467-476.
9. Conway J.H., Sloane N.J.A. Sphere Packings, Lattices and Groups. 3rd Edition:1999;Springer, New York.
10. Forney G. Jr. Dimension. / length profiles and trellis complexity of linear block codes IEEE Trans. Inform. Theory. 40(6):1994;1741-1752.
11. Forney G. Jr. Density. / length profiles and trellis complexity of lattices IEEE Trans. Inform. Theory. 40(6):1994;1753-1772.
12. I.M. Gelfand, M.I. Graev, N. Ya, Vilenkin, Generalized Functions, Integral Geometry and Representation Theory, Vol. 5, Academic Press, New York, London, (1966) [1977].
13. M. Gromov, Systoles and intersystolic inequalities, preprint IHES / M / 92 / 98, 1992.
14. Helgason S. Groups and Geometric Analysis. Integral Geometry, Invariant Differential Operators, and Spherical Functions. 1984;Academic Press, New York.
15. Helgason S. Geometric Analysis on Symmetric Spaces. 1994;AMS, Providence, RI.
16. l-1)/N ) Discrete Math. 18:1977;179-211.
17. Helleseth T., Kl ø ve T., Ytrehus Ø., Levenshtein V. Bounds on the minimum support weights. IEEE Trans. Inform. Theory. 41:1995;432-440.
18. Kl ø ve T. Support weight distribution of linear codes. Discrete Math. 106 / 107:1992;311-313.
19. M. Lavrentjev, L. Saveljev, Linear Operators and Ill-Posed Problems, With a Supplement by A.L. Bukhgeim, Consultants Bureau, New York, 1995.
20. MacWilliams F.J., Sloane N.J.A. The Theory of Error-Correcting Codes. 1977;Elsevier, Amsterdam.
21. D. Nogin, Weight / multiplicity duality, Proceedings of the Sixth International Workshop "Algebraic and Combinatorial Coding Theory", Pskov, Russia, September 1998, pp. 195-198.
22. Radon J. Über die Bestimmung von Funktionen durch ihre Integralwärte längs gewisser Männigfretigkeiten. Ber. Verh. Sc̈hs. Akad. 69:1917;262-277.
23. Rankin R. On positive definite quadratic forms. J. London Math. Soc. 28:1953;309-314.
24. Siegel K.L. A mean value theorem in geometry of numbers. Ann. Math. 46:1945;340-347.
25. Simonis J. The effective length of subcodes. Appl. Algebra Eng. Comm. Comput. 5:1994;371-377.
26. Thunder J. Higher-dimensional analogs of Hermite's constant. Michigan Math. J. 45(2):1998;301-314.
27. Thunder J. An adelic Minkowski-Hlawka theorem and an application to Siegel's lemma. J. Reine Angew. Math. 475:1996;167-185.
28. Tsfasman M., Vladut S. Geometric approach to higher weights. IEEE Trans. Inform. Theory. 41:1995;1564-1588.
29. G. van der Geer, M. van der Vlugt, Generalized Reed-Muller codes and curves with many points, alg-geom / 9710016.
30. Wei V.K. Generalized Hamming weights for linear codes. IEEE Trans. Inform. Theory. 38:1992;1125-1130.
31. V.K. Wei, Generalized Hamming weights; Fundamental open problems in coding theory, in: Arithmetic, Geometry and Coding Theory, Walter de Gruyter, Berlin, 1996, pp. 269-281.