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Articles

Construction of s-extremal optimal unimodular lattices in dimension 52

Pages 87-91 | Received 30 Dec 2019, Accepted 02 Apr 2020, Published online: 29 Apr 2020

References

  • W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24 (1997), pp. 235–265. doi: 10.1006/jsco.1996.0125
  • J.H. Conway and N.J.A. Sloane, A note on optimal unimodular lattices, J. Number Theory 72 (1998), pp. 357–362. doi: 10.1006/jnth.1998.2257
  • J.H. Conway and N.J.A. Sloane, Sphere Packing, Lattices and Groups, 3rd ed., Springer-Verlag, New York, 1999.
  • S.T. Dougherty, M. Harada, and P. Solé, Shadow lattices and shadow codes, Discrete Math. 219 (2000), pp. 49–64. doi: 10.1016/S0012-365X(99)00368-4
  • P. Gaborit, Construction of new extremal unimodular lattices, Eur. J. Combin. 25 (2004), pp. 549–564. doi: 10.1016/j.ejc.2003.07.005
  • P. Gaborit, A bound for certain s-extremal lattices and codes, Arch. Math. 89 (2007), pp. 143–151. doi: 10.1007/s00013-006-1164-5
  • M. Harada, Construction of some unimodular lattices with long shadows, Int. J. Number Theory 7 (2011), pp. 1345–1358. doi: 10.1142/S1793042111004794
  • M. Harada, M. Kitazume, A. Munemasa, and B. Venkov, On some self-dual codes and unimodular lattices in dimension 48, Eur. J. Combin. 26 (2005), pp. 543–557. doi: 10.1016/j.ejc.2004.06.013
  • M. Harada, W. Holzmann, H. Kharaghani, and M. Khorvash, Extremal ternary self-dual codes constructed from negacirculant matrices, Graphs Combin. 23 (2007), pp. 401–417. doi: 10.1007/s00373-007-0731-2
  • G. Nebe and N.J.A. Sloane, Unimodular lattices, together with a table of the best such lattices, in A Catalogue of Lattices, published electronically at http://www.math.rwth-aachen.de/ Gabriele.Nebe/LATTICES/.

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