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On skew polynomial codes and lattices from quotients of cyclic division algebras
1. | Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore |
References:
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D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Engin. Commun. Comput., 18 (2007), 379-389.
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D. Boucher and F. Ulmer, Coding with skew polynomial rings, J. Symb. Comput., 44 (2009), 1644-1656.
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D. Boucher, F. Ulmer and P. Solé, Skew constacyclic codes over Galois rings, Adv. Math. Commun., 2 (2008), 273-292.
doi: 10.3934/amc.2008.2.273. |
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J. H. Conway and N. J. A Sloane, Sphere Packings, Lattices and Groups,, Springer., ().
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J. Ducoat and F. Oggier, Lattice encoding of cyclic codes from skew-polynomial rings, in Coding Theory and Applications, Springer, 2015, 161-167. |
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W. Ebeling, Lattices and Codes, A Course Partially Based on Lectures by Friedrich Hirzebruch, Springer, 2013.
doi: 10.1007/978-3-658-00360-9. |
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G. D. Forney, Coset Codes Part I: Introduction and geometrical classification, IEEE Trans. Inf. Theory, 34 (1988), 1123-1151.
doi: 10.1109/18.21245. |
[13] |
F. Oggier and J.-C. Belfiore, Enabling multiplication in lattice codes via construction A, in IEEE Int. Workshop Inf. Theory, 2013, 1-5. |
[14] |
F. Oggier and B. A. Sethuraman, Quotients of orders in cyclic algebras and space-time codes, Adv. Math. Commun., 7 (2013), 441-461.
doi: 10.3934/amc.2013.7.441. |
[15] |
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. |
show all references
References:
[1] | |
[2] |
C. Bachoc, Applications of coding theory to the construction of modular lattices, J. Combin. Theory Ser. A, 78 (1997), 92-119.
doi: 10.1006/jcta.1996.2763. |
[3] |
J.-C. Belfiore and F. Oggier, An error probability approach to MIMO wiretap channels, IEEE Trans. Commun., 61 (2013), 3396-3403. |
[4] |
G. Berhuy and F. Oggier, An Introduction to Central Simple Algebras and Their Applications to Wireless Communication, AMS, 2013.
doi: 10.1090/surv/191. |
[5] |
A. Bonnecaze, P. Solé and A. R. Calderbank, Quaternary qudratic residue codes and unimodular lattices, IEEE Trans. Inf. Theory, 41 (1995), 366-377.
doi: 10.1109/18.370138. |
[6] |
D. Boucher, W. Geiselmann and F. Ulmer, Skew cyclic codes, Appl. Algebra Engin. Commun. Comput., 18 (2007), 379-389.
doi: 10.1007/s00200-007-0043-z. |
[7] |
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. |
[8] |
D. Boucher, F. Ulmer and P. Solé, Skew constacyclic codes over Galois rings, Adv. Math. Commun., 2 (2008), 273-292.
doi: 10.3934/amc.2008.2.273. |
[9] |
J. H. Conway and N. J. A Sloane, Sphere Packings, Lattices and Groups,, Springer., ().
|
[10] |
J. Ducoat and F. Oggier, Lattice encoding of cyclic codes from skew-polynomial rings, in Coding Theory and Applications, Springer, 2015, 161-167. |
[11] |
W. Ebeling, Lattices and Codes, A Course Partially Based on Lectures by Friedrich Hirzebruch, Springer, 2013.
doi: 10.1007/978-3-658-00360-9. |
[12] |
G. D. Forney, Coset Codes Part I: Introduction and geometrical classification, IEEE Trans. Inf. Theory, 34 (1988), 1123-1151.
doi: 10.1109/18.21245. |
[13] |
F. Oggier and J.-C. Belfiore, Enabling multiplication in lattice codes via construction A, in IEEE Int. Workshop Inf. Theory, 2013, 1-5. |
[14] |
F. Oggier and B. A. Sethuraman, Quotients of orders in cyclic algebras and space-time codes, Adv. Math. Commun., 7 (2013), 441-461.
doi: 10.3934/amc.2013.7.441. |
[15] |
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. |
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