There is no Euclidean self-dual quaternary [18,9,7] code (Q622783)

Summary: 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.