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The applications of additive codes mainly lie in quantum error correction andquantum computing. Due to their applications in quantum codes, additive codeshave grown in importance. In addition to this, additive codes allow theimplementation of a variety of dualities. The article begins by developing theproperties of Additive Complementary Dual (ACD) codes with respect to arbitrarydualities over finite abelian groups. Further, we introduce a subclass ofnon-symmetric dualities referred to as skew-symmetric dualities. Then, weprecisely count symmetric and skew-symmetric dualities over finite fields. Twoconditions have been obtained: one is a necessary and sufficient condition, andthe other is a necessary condition. The necessary and sufficient condition isfor an additive code to be an ACD code over arbitrary dualities. The necessarycondition is on the generator matrix of an ACD code over skew-symmetricdualities. We provide bounds for the highest possible minimum distance of ACDcodes over skew-symmetric dualities. Finally, we find some new quaternary ACDcodes over non-symmetric dualities with better parameters than the symmetricones.

ACD codes over skew-symmetric dualities