|
[1]
|
C. Bachoc, Applications of coding theory to the construction of modular lattices, Journal of Combinatorial Theory, 78 (1997), 92-119.
doi: 10.1006/jcta.1996.2763.
|
|
[2]
|
E. Bayer-Fluckiger, Ideal lattices, A Panorama of Number Theory or The View from Baker's Garden, edited by Gisbert Wustholz Cambridge Univ. Press, Cambridge, (2002), 168-184.
|
|
[3]
|
E. Bayer-Fluckiger and I. Suarez, Modular lattices over cyclotomic fields, Journal of Number Theory, 114 (2005), 394-411.
doi: 10.1016/j.jnt.2004.10.005.
|
|
[4]
|
V. Blomer, Uniform bounds for Fourier coefficients of theta-series with arithmetic applications, Acta Arithmetica, 114 (2004), 1-21.
doi: 10.4064/aa114-1-1.
|
|
[5]
|
S. Böcherer and G. Nebe, On theta series attached to maximal lattices and their adjoints, J.ramanujan Math.soc, 25 (2010), 265-284.
|
|
[6]
|
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. Ⅰ. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125.
|
|
[7]
|
R. Chapman, S. T. Dougherty, P. Gaborit and P. Solé, 2-modular lattices from ternary codes, Journal De Théorie Des Nombres De Bordeaux, 14 (2002), 73-85.
doi: 10.5802/jtnb.347.
|
|
[8]
|
K. S. Chua and P. Solé, Eisenstein lattices, Galois rings, and Theta Series, European Journal of Combinatorics, 25 (2004), 179-185.
doi: 10.1016/S0195-6698(03)00098-2.
|
|
[9]
|
J. H. Conway and N. J. A. Sloane,
Sphere Packings, Lattices and Groups, Springer, New York, 1988.
doi: 10. 1007/978-1-4757-6568-7.
|
|
[10]
|
J. H. Conway and N. J. A. Sloane, A new upper bound for the minimum of an integral lattice of determinant one, Bull. Amer. Math. Soc., 23 (1990), 383-387.
doi: 10.1090/S0273-0979-1990-15940-3.
|
|
[11]
|
J. H. Conway and N. J. A. Sloane, A note on optimal unimodular lattices, J. Number Theory, 72 (1998), 357-362.
doi: 10.1006/jnth.1998.2257.
|
|
[12]
|
W. Ebeling,
Lattices and Codes: A Course Partially Based on Lecturers by F. Hirzebruch Advanced Lectures in Mathematics, Springer, Germany, 2013.
doi: 10.1007/978-3-658-00360-9.
|
|
[13]
|
A.-M. Ernvall-Hytönen, On a conjecture by Belfiore and Sol´e on some lattices, IEEE Trans. Inf. Theory, 58 (2012), 5950-5955.
doi: 10.1109/TIT.2012.2201915.
|
|
[14]
|
G. D. Forney, Coset codes-part Ⅰ: Introduction and geometrical classification, IEEE Trans. Inform. Theory, 34 (1988), 1123-1151.
doi: 10.1109/18.21245.
|
|
[15]
|
X. Hou, F. Lin and F. Oggier, Construction and secrecy gain of a family of 5−modular lattices, in the proceedings of the IEEE Information Theory Workshop, (2014), 117-121.
doi: 10.1109/ITW.2014.6970804.
|
|
[16]
|
W. Kositwattanarerk, S. S. Ong and F. Oggier, Construction a of lattices over number fields and block fading wiretap coding, IEEE Transactions on Information Theory, 61 (2015), 2273-2282.
doi: 10.1109/TIT.2015.2416340.
|
|
[17]
|
F. Lin and F. Oggier, A classification of unimodular lattice wiretap codes in small dimensions, IEEE Trans. Inf. Theory, 59 (2013), 3295-3303.
doi: 10.1109/TIT.2013.2246814.
|
|
[18]
|
F. Lin, F. Oggier and P. Solé, 2-and 3-modular lattice wiretap codes in small dimensions, Applicable Algebra in Engineering, Communication and Computing, 26 (2015), 571-590.
doi: 10.1007/s00200-015-0267-2.
|
|
[19]
|
S. Ling and C. Xing,
Coding Theory: A First Course, Cambridge University Press, 2004.
doi: 10.1017/CBO9780511755279.
|
|
[20]
|
C. L. Mallows, A. M. Odlyzko and N. J. A. Sloane, Upper bounds for modular forms, lattices and codes, Journal of Algebra, 36 (1975), 68-76.
doi: 10.1016/0021-8693(75)90155-6.
|
|
[21]
|
G. Nebe, Finite subgroups of GL$_{24}(\mathbb{Q})$, Experimental Mathematics, 5 (1996), 163-195.
|
|
[22]
|
G. Nebe, Finite subgroups of GL$_n(\mathbb{Q})$ for $25≤n≤31$, Communications in Algebra, 24 (1996), 2341-2397.
|
|
[23]
|
G. Nebe and K. Schindelar, S-extremal strongly modular lattices, Journal de théorie des nombres de Bordeaux, 19 (2007), 683-701.
doi: 10.5802/jtnb.608.
|
|
[24]
|
G. Nebe, Automorphisms of extremal unimodular lattices in dimension 72, Journal of Number Theory, 161 (2016), 362-383.
doi: 10.1016/j.jnt.2015.05.001.
|
|
[25]
|
J. Neukirch,
Algebraic Number Theory, Springer-Verlag, New York, 1999.
doi: 10.1007/978-3-662-03983-0.
|
|
[26]
|
F. Oggier and E. Viterbo, Algebraic number theory and code design for Rayleigh fading channels, Foundations and Trends in Communications and Information Theory, 1 (2004), 333-415.
doi: 10.1561/0100000003.
|
|
[27]
|
F. Oggier, P. Solé and J.-C. Belfiore, Lattice codes for the wiretap Gaussian channel: Construction and analysis, IEEE Transactions on Information Theory, 62 (2016), 5690-5708.
doi: 10.1109/TIT.2015.2494594.
|
|
[28]
|
F. Oggier and J. -C. Belfiore, Enabling multiplication in lattice codes via Construction A, in the proceedings of the IEEE Information Theory Workshop, 2013 (ITW), 9-13.
|
|
[29]
|
J. Pinchak and B. A. Sethuraman, The Belfiore-Solé Conjecture and a certain technique for verifying it for a given lattice, Information Theory and Applications, (2014), 1-3.
doi: 10.1109/ITA.2014.6804279.
|
|
[30]
|
H.-G. Quebbemann, Atkin-Lehner eigenforms and strongly modular lattices, L'Enseign. Math., 43 (1997), 55-65.
|
|
[31]
|
H.-G. Quebbemann, A shadow identity and an application to isoduality, Abhandlungen aus dem mathematischen Seminar der Universität Hamburg, 68 (1998), 339-345.
doi: 10.1007/BF02942571.
|
|
[32]
|
E. Rains and N. J. A. Sloane, The shadow theory of modular and unimodular lattices, Journal of Number Theory, 73 (1999), 359-389.
doi: 10.1006/jnth.1998.2306.
|
|
[33]
|
SageMath, The Sage Mathematics Software System (Version 7. 1), The Sage Developers, 2016, http://www.sagemath.org.
|
|
[34]
|
N. J. A. Sloane, Codes over GF(4) and complex lattices, Journal of Algebra, 52 (1978), 168-181.
doi: 10.1016/0021-8693(78)90266-1.
|
|
[35]
|
N. J. A. Sloane and G. Nebe, Catalogue of Lattices, published electronically at http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/.
|
|
[36]
|
Wolfram Research, Inc., Mathematica, Version 10. 4, Champaign, IL, 2016.
|
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