Agradecimentos: The authors would like to thank the reviewers for their comments and suggestions

Abstract: We investigate perfect codes in in the metric. Upper bounds for the packing radius of a linear perfect code, in terms of the metric parameter and the dimension are derived. For and , we determine all radii for which there exist linear perfect codes. The non-existence results for...

Abstract: We investigate perfect codes in in the metric. Upper bounds for the packing radius of a linear perfect code, in terms of the metric parameter and the dimension are derived. For and , we determine all radii for which there exist linear perfect codes. The non-existence results for codes in presented here imply non-existence results for codes over finite alphabets , when the alphabet size is large enough, and have implications on some recent constructions of spherical codes

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP

2014/20602-8; 2013/25977-7

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ

312926/2013-8

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