Abstract
A construction of laminated lattices of full diversity in odd dimensions with is presented. The technique, which uses a combination of number fields and error-correcting codes, consists essentially of two steps: In the first, the Abelian number field of degree and prime conductor , where is a prime congruent to 1 modulo , is considered. In the second, the lattice is obtained as the canonical embedding (Minkowski homomorphism) of a -submodule of , the ring of integers of . The submodule is defined by the parity-check matrices of a Reed–Solomon code over and a suitably chosen linear code, typically either binary or over , the ring of integers modulo 4.
Citation
J. Carmelo Interlando. Trajano Pires da Nóbrega Neto. José Valter Lopes Nunes. José Othon Dantas Lopes. "Lattices from Abelian extensions and error-correcting codes." Rocky Mountain J. Math. 51 (3) 903 - 920, June 2021. https://doi.org/10.1216/rmj.2021.51.903
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