Multi-twisted additive codes with complementary duals over finite fields

Multi-twisted (MT) additive codes over finite fields form an important class of additive codes and are generalizations of constacyclic additive codes. In this paper, we study a special class of MT additive codes over finite fields, namely complementary-dual MT additive codes (or MT additive codes with complementary duals) by placing ordinary, Hermitian, and $\ast$ trace bilinear forms. We also derive a necessary and sufficient condition for an MT additive code over a finite field to have a complementary dual. We further provide explicit enumeration formulae for all complementary-dual MT additive codes over finite fields with respect to the aforementioned trace bilinear forms. We also illustrate our results with some examples.