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On the dual of (non)-weakly regular bent functions and self-dual bent functions
Quotients of orders in cyclic algebras and space-time codes
1. | Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore |
2. | Department of Mathematics, California State University Northridge, Northridge, CA 91330, United States |
References:
[1] |
J.-C. Belfiore and F. Oggier, An error probability approach to MIMO wiretap channels, IEEE Trans. Commun., 61 (2013), 3396-3403.
doi: 10.1109/TCOMM.2013.061913.120278. |
[2] |
D. Boucher and F. Ulmer, Coding with skew polynomial rings, J. Symb. Comput., 44 (2009), 1644-1656.
doi: 10.1016/j.jsc.2007.11.008. |
[3] |
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1999. |
[4] |
B. Jacob and A. Wadsworth, Division algebras over Henselian fields, J. Algebra, 128 (1990), 126-179.
doi: 10.1016/0021-8693(90)90047-R. |
[5] |
G. J. Janusz, Algebraic Number Fields, Second edition, Amer. Math. Soc., 1996. |
[6] |
L. Luzzi, G. R. B. Othman, J. C. Belfiore and E. Viterbo, Golden space-time block-coded modulation, IEEE Trans. Inf. Theory, 55 (2009), 584-597.
doi: 10.1109/TIT.2008.2009846. |
[7] |
G. Nebe, E. M. Rains and N. J. A. Sloane, Codes and Invariant Theory, Math. Nachrichten, 274 (2004), 104-116.
doi: 10.1002/mana.200310204. |
[8] |
F. Oggier, G. Rekaya, J.-C. Belfiore and E. Viterbo, Perfect space time block codes, IEEE Trans. Inf. Theory, 52 (2006), 3885-3902.
doi: 10.1109/TIT.2006.880010. |
[9] |
F. Oggier, P. Solé and J.-C. Belfiore, Codes over matrix rings for space-time coded modulations, IEEE Trans. Inf. Theory, 58 (2012), 734-746.
doi: 10.1109/TIT.2011.2173732. |
[10] | |
[11] | |
[12] |
O. F. G. Schilling, The Theory of Valuations, Amer. Math. Soc., 1950. |
[13] |
B. A. Sethuraman, Division algebras and wireless communication, Notices AMS, 57 (2010), 1432-1439. |
[14] |
B. A. Sethuraman, B. S. Rajan and V. Shashidhar, Full-diversity, high-rate space-time block codes from division algebras, IEEE Trans. Inf. Theory, 49 (2003), 2596-2616.
doi: 10.1109/TIT.2003.817831. |
[15] |
A. Wadsworth, Valuation theory on finite dimensional division algebras, Fields Institute Commu., 32 (2002), 385-449. |
[16] |
L. C. Washington, Introduction to Ceyclotomic Fields, Springer, 1982.
doi: 10.1007/978-1-4684-0133-2. |
[17] |
A. D. Wyner, The wire-tap channel, Bell Syst. Tech. J., 54 (1975), 1355-1387.
doi: 10.1002/j.1538-7305.1975.tb02040.x. |
show all references
References:
[1] |
J.-C. Belfiore and F. Oggier, An error probability approach to MIMO wiretap channels, IEEE Trans. Commun., 61 (2013), 3396-3403.
doi: 10.1109/TCOMM.2013.061913.120278. |
[2] |
D. Boucher and F. Ulmer, Coding with skew polynomial rings, J. Symb. Comput., 44 (2009), 1644-1656.
doi: 10.1016/j.jsc.2007.11.008. |
[3] |
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1999. |
[4] |
B. Jacob and A. Wadsworth, Division algebras over Henselian fields, J. Algebra, 128 (1990), 126-179.
doi: 10.1016/0021-8693(90)90047-R. |
[5] |
G. J. Janusz, Algebraic Number Fields, Second edition, Amer. Math. Soc., 1996. |
[6] |
L. Luzzi, G. R. B. Othman, J. C. Belfiore and E. Viterbo, Golden space-time block-coded modulation, IEEE Trans. Inf. Theory, 55 (2009), 584-597.
doi: 10.1109/TIT.2008.2009846. |
[7] |
G. Nebe, E. M. Rains and N. J. A. Sloane, Codes and Invariant Theory, Math. Nachrichten, 274 (2004), 104-116.
doi: 10.1002/mana.200310204. |
[8] |
F. Oggier, G. Rekaya, J.-C. Belfiore and E. Viterbo, Perfect space time block codes, IEEE Trans. Inf. Theory, 52 (2006), 3885-3902.
doi: 10.1109/TIT.2006.880010. |
[9] |
F. Oggier, P. Solé and J.-C. Belfiore, Codes over matrix rings for space-time coded modulations, IEEE Trans. Inf. Theory, 58 (2012), 734-746.
doi: 10.1109/TIT.2011.2173732. |
[10] | |
[11] | |
[12] |
O. F. G. Schilling, The Theory of Valuations, Amer. Math. Soc., 1950. |
[13] |
B. A. Sethuraman, Division algebras and wireless communication, Notices AMS, 57 (2010), 1432-1439. |
[14] |
B. A. Sethuraman, B. S. Rajan and V. Shashidhar, Full-diversity, high-rate space-time block codes from division algebras, IEEE Trans. Inf. Theory, 49 (2003), 2596-2616.
doi: 10.1109/TIT.2003.817831. |
[15] |
A. Wadsworth, Valuation theory on finite dimensional division algebras, Fields Institute Commu., 32 (2002), 385-449. |
[16] |
L. C. Washington, Introduction to Ceyclotomic Fields, Springer, 1982.
doi: 10.1007/978-1-4684-0133-2. |
[17] |
A. D. Wyner, The wire-tap channel, Bell Syst. Tech. J., 54 (1975), 1355-1387.
doi: 10.1002/j.1538-7305.1975.tb02040.x. |
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