There is no Euclidean self-dual quaternary [18,9,7] code
by Carlos Aguilar, Christophe Chabot, Philippe Gaborit
International Journal of Information and Coding Theory (IJICOT), Vol. 1, No. 2, 2010

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.

Online publication date: Wed, 10-Mar-2010

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