Multi-twisted additive codes over finite fields

Abstract

In this paper, we introduce a new class of additive codes over finite fields, viz. multi-twisted (MT) additive codes, which are generalizations of constacyclic additive codes. We study their algebraic structures by writing a canonical form decomposition and provide an enumeration formula for these codes. By placing ordinary, Hermitian and $$*$$ trace bilinear forms, we further study their dual codes and derive necessary and sufficient conditions under which a MT additive code is self-dual and self-orthogonal. We also derive a necessary and sufficient condition for the existence of a self-dual MT additive code over a finite field, and provide enumeration formulae for all self-dual and self-orthogonal MT additive codes over finite fields with respect to the aforementioned trace bilinear forms. We also obtain several good codes within the family of MT additive codes over finite fields.