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Article Dans Une Revue International Journal of Information and Coding Theory Année : 2010

There is no Euclidean self-dual quaternary [18,9,7] code

Résumé

In this paper, we prove that there is no Euclidean self-dual quaternary [18, 9, 7] code for the Hamming distance. The proof is based on a generalisation of the balance principle to Euclidean self-dual quaternary codes. We prove that the existence of an [18, 9, 7] Euclidean self-dual quaternary code implies the existence of an [11, 3, 7] Euclidean self-orthogonal code, which non-existence is proven. We give an up-to-date table for Euclidean self-dual quaternary codes.
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hal-00712945 , version 1 (28-06-2012)

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Carlos Aguilar Melchor, Christophe Chabot, Philippe Gaborit. There is no Euclidean self-dual quaternary [18,9,7] code. International Journal of Information and Coding Theory, 2010, 1 (2), pp.200-207. ⟨10.1504/IJICOT.2010.032135⟩. ⟨hal-00712945⟩
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