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Universal codes and unimodular lattices

Robin ChapmanPatrick Solé — 1996

Journal de théorie des nombres de Bordeaux

Binary quadratic residue codes of length p + 1 produce via construction B and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction A modulo 4 . We prove in a direct way the equivalence of these two constructions for p 31 . In dimension 32, we obtain an extremal lattice of type II not isometric to the Barnes-Wall lattice B W 32 . The equivalence between construction B modulo 4 plus density doubling and construction...

2 -modular lattices from ternary codes

Robin ChapmanSteven T. DoughertyPhilippe GaboritPatrick Solé — 2002

Journal de théorie des nombres de Bordeaux

The alphabet 𝐅 3 + v 𝐅 3 where v 2 = 1 is viewed here as a quotient of the ring of integers of 𝐐 ( - 2 ) by the ideal (3). Self-dual 𝐅 3 + v 𝐅 3 codes for the hermitian scalar product give 2 -modular lattices by construction A K . There is a Gray map which maps self-dual codes for the Euclidean scalar product into Type III codes with a fixed point free involution in their automorphism group. Gleason type theorems for the symmetrized weight enumerators of Euclidean self-dual codes and the length weight enumerator of hermitian self-dual...

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