Lattices from maximal orders into quaternion algebras

• C. Alves ^[1] ; J.-C. Belfiore ^[2]
  1. [1] Universidade Estadual Paulista

     Universidade Estadual Paulista

     Brasil

     
  2. [2] TELECOM-Paris Tech (France)
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 4 ((April 2015) ), 2015, págs. 687-702
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.04.025
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• Resumen

  • We propose an algebraic framework to construct dense lattices from maximal orders of a quaternion algebra whose center is an imaginary quadratic field. This work extends [21] where a method called algebraic reduction has been proposed to efficiently decode the Golden code [14]. In particular, we propose four new constructions of E8E8 lattice from left ideals of maximal orders of some quaternion algebras with centers Q(−d), d=1,2,3,7d=1,2,3,7.