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We study additive quaternary codes whose parameters are close to those of theextended cyclic [12; 6; 6]4-code or to the quaternary linear codes generated bythe elliptic quadric in PG(3; 4) or its dual. In particular we characterizethose codes in the category of additive codes and construct some additive codeswhose parameters are better than those of any linear quaternary code.

Additive quaternary codes related to exceptional linear quaternary codes