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Enumeration of self-dual and self-orthogonal negacyclic codes over finite fields
The nonassociative algebras used to build fast-decodable space-time block codes
1. | School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD |
2. | Flat 203, Wilson Tower, 16 Christian Street, London E1 1AW, United Kingdom |
References:
[1] |
V. Astier and S. Pumplün, Nonassociative quaternion algebras over rings, Israel J. Math., 155 (2006), 125-147.
doi: 10.1007/BF02773952. |
[2] |
C. Brown, PhD Thesis University of Nottingham,, in preparation., ().
|
[3] |
N. Jacobson, Finite-dimensional Division Algebras Over Fields, Springer Verlag, Berlin-Heidelberg-New York, 1996.
doi: 10.1007/978-3-642-02429-0. |
[4] |
G. R. Jithamitra and B. S. Rajan, Minimizing the complexity of fast-sphere decoding of STBCs, IEEE Int. Symposium on Information Theory Proceedings (ISIT), (2011), 1846-1850.
doi: 10.1109/ISIT.2011.6033869. |
[5] |
M. A. Knus, A. Merkurjev, M. Rost and J.-P. Tignol, The Book of Involutions, AMS Coll. Publications, 44, 1998. |
[6] |
N. Markin and F. Oggier, Iterated space-time code constructions from cyclic algebras, IEEE Trans. Inf. Theory, 59 (2013), 5966-5979.
doi: 10.1109/TIT.2013.2266397. |
[7] |
L. P. Natarajan and B. S. Rajan, Fast group-decodable STBCs via codes over GF(4), Proc. IEEE Int. Symp. Inform. Theory, Austin, TX, (2010), 1056-1060.
doi: 10.1109/ISIT.2010.5513721. |
[8] |
L. P. Natarajan and B. S. Rajan, Fast-Group-Decodable STBCs via codes over GF(4): Further results, Proceedings of IEEE ICC 2011, (ICC'11), Kyoto, Japan, (2011), 1-6.
doi: 10.1109/icc.2011.5962874. |
[9] |
L. P. Natarajan and B. S. Rajan, written communication,, 2013., ().
|
[10] |
J.-C. Petit, Sur certains quasi-corps généralisant un type d'anneau-quotient,, Séminaire Dubriel. Algèbre et théorie des nombres, 20 (): 1.
|
[11] |
S. Pumplün and A. Steele, Fast-decodable MIDO codes from nonassociative algebras, Int. J. of Information and Coding Theory (IJICOT), 3 (2015), 15-38.
doi: 10.1504/IJICOT.2015.068695. |
[12] |
S. Pumplün, How to obtain division algebras used for fast decodable space-time block codes, Adv. Math. Comm., 8 (2014), 323-342.
doi: 10.3934/amc.2014.8.323. |
[13] |
S. Pumplün, Tensor products of nonassociative cyclic algebras,, Online at , ().
|
[14] |
S. Pumplün and T. Unger, Space-time block codes from nonassociative division algebras, Adv. Math. Comm., 5 (2011), 449-471.
doi: 10.3934/amc.2011.5.449. |
[15] |
K. P. Srinath and B. S. Rajan, DMT-optimal, low ML-complexity STBC-schemes for asymmetric MIMO systems, 2012 IEEE International Symposium on Information Theory Proceedings (ISIT), (2012), 3043-3047.
doi: 10.1109/ISIT.2012.6284120. |
[16] |
K. P. Srinath and B. S. Rajan, Fast-decodable MIDO codes with large coding gain, IEEE Transactions on Information Theory, 60 (2014), 992-1007.
doi: 10.1109/TIT.2013.2292513. |
[17] |
R. D. Schafer, An Introduction to Nonassociative Algebras, Dover Publ., Inc., New York, 1995. |
[18] |
A. Steele, Nonassociative cyclic algebras, Israel J. Math., 200 (2014), 361-387.
doi: 10.1007/s11856-014-0021-7. |
[19] |
A. Steele, S. Pumplün and F. Oggier, MIDO space-time codes from associative and non-associative cyclic algebras, Information Theory Workshop (ITW) 2012 IEEE, (2012), 192-196. |
[20] |
R. Vehkalahti, C. Hollanti and F. Oggier, Fast-decodable asymmetric space-time codes from division algebras, IEEE Transactions on Information Theory, 58 (2012), 2362-2385.
doi: 10.1109/TIT.2011.2176310. |
[21] |
W. C. Waterhouse, Nonassociative quaternion algebras, Algebras Groups Geom., 4 (1987), 365-378. |
show all references
References:
[1] |
V. Astier and S. Pumplün, Nonassociative quaternion algebras over rings, Israel J. Math., 155 (2006), 125-147.
doi: 10.1007/BF02773952. |
[2] |
C. Brown, PhD Thesis University of Nottingham,, in preparation., ().
|
[3] |
N. Jacobson, Finite-dimensional Division Algebras Over Fields, Springer Verlag, Berlin-Heidelberg-New York, 1996.
doi: 10.1007/978-3-642-02429-0. |
[4] |
G. R. Jithamitra and B. S. Rajan, Minimizing the complexity of fast-sphere decoding of STBCs, IEEE Int. Symposium on Information Theory Proceedings (ISIT), (2011), 1846-1850.
doi: 10.1109/ISIT.2011.6033869. |
[5] |
M. A. Knus, A. Merkurjev, M. Rost and J.-P. Tignol, The Book of Involutions, AMS Coll. Publications, 44, 1998. |
[6] |
N. Markin and F. Oggier, Iterated space-time code constructions from cyclic algebras, IEEE Trans. Inf. Theory, 59 (2013), 5966-5979.
doi: 10.1109/TIT.2013.2266397. |
[7] |
L. P. Natarajan and B. S. Rajan, Fast group-decodable STBCs via codes over GF(4), Proc. IEEE Int. Symp. Inform. Theory, Austin, TX, (2010), 1056-1060.
doi: 10.1109/ISIT.2010.5513721. |
[8] |
L. P. Natarajan and B. S. Rajan, Fast-Group-Decodable STBCs via codes over GF(4): Further results, Proceedings of IEEE ICC 2011, (ICC'11), Kyoto, Japan, (2011), 1-6.
doi: 10.1109/icc.2011.5962874. |
[9] |
L. P. Natarajan and B. S. Rajan, written communication,, 2013., ().
|
[10] |
J.-C. Petit, Sur certains quasi-corps généralisant un type d'anneau-quotient,, Séminaire Dubriel. Algèbre et théorie des nombres, 20 (): 1.
|
[11] |
S. Pumplün and A. Steele, Fast-decodable MIDO codes from nonassociative algebras, Int. J. of Information and Coding Theory (IJICOT), 3 (2015), 15-38.
doi: 10.1504/IJICOT.2015.068695. |
[12] |
S. Pumplün, How to obtain division algebras used for fast decodable space-time block codes, Adv. Math. Comm., 8 (2014), 323-342.
doi: 10.3934/amc.2014.8.323. |
[13] |
S. Pumplün, Tensor products of nonassociative cyclic algebras,, Online at , ().
|
[14] |
S. Pumplün and T. Unger, Space-time block codes from nonassociative division algebras, Adv. Math. Comm., 5 (2011), 449-471.
doi: 10.3934/amc.2011.5.449. |
[15] |
K. P. Srinath and B. S. Rajan, DMT-optimal, low ML-complexity STBC-schemes for asymmetric MIMO systems, 2012 IEEE International Symposium on Information Theory Proceedings (ISIT), (2012), 3043-3047.
doi: 10.1109/ISIT.2012.6284120. |
[16] |
K. P. Srinath and B. S. Rajan, Fast-decodable MIDO codes with large coding gain, IEEE Transactions on Information Theory, 60 (2014), 992-1007.
doi: 10.1109/TIT.2013.2292513. |
[17] |
R. D. Schafer, An Introduction to Nonassociative Algebras, Dover Publ., Inc., New York, 1995. |
[18] |
A. Steele, Nonassociative cyclic algebras, Israel J. Math., 200 (2014), 361-387.
doi: 10.1007/s11856-014-0021-7. |
[19] |
A. Steele, S. Pumplün and F. Oggier, MIDO space-time codes from associative and non-associative cyclic algebras, Information Theory Workshop (ITW) 2012 IEEE, (2012), 192-196. |
[20] |
R. Vehkalahti, C. Hollanti and F. Oggier, Fast-decodable asymmetric space-time codes from division algebras, IEEE Transactions on Information Theory, 58 (2012), 2362-2385.
doi: 10.1109/TIT.2011.2176310. |
[21] |
W. C. Waterhouse, Nonassociative quaternion algebras, Algebras Groups Geom., 4 (1987), 365-378. |
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