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

Authors: Carlos Aguilar, Christophe Chabot, Philippe Gaborit

Addresses: XLIM-DMI, University of Limoges, 123 avenue Albert Thomas, Limoges 87000, France. ' IRMAR, University of Rennes I, Campus de Beaulieu, Rennes Cedex 35042, France. ' XLIM-DMI, University of Limoges, 123 avenue Albert Thomas, Limoges 87000, France

Abstract: 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.

Keywords: quaternary self-dual codes; bounds; Euclidean self-dual codes; Hamming distance.

DOI: 10.1504/IJICOT.2010.032135

International Journal of Information and Coding Theory, 2010 Vol.1 No.2, pp.200 - 207

Published online: 10 Mar 2010 *

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