Constacyclic additive codes over finite fields

Abstract

Let [Formula: see text] denote the finite field of order [Formula: see text] and characteristic [Formula: see text] [Formula: see text] be a positive integer coprime to [Formula: see text] and let [Formula: see text] be an integer. In this paper, we develop the theory of constacyclic additive codes of length [Formula: see text] over [Formula: see text] and provide a canonical form decomposition for these codes. By placing ordinary, Hermitian and ∗ trace bilinear forms on [Formula: see text] we determine some isodual constacyclic additive codes of length [Formula: see text] over [Formula: see text] Moreover, we explicitly determine basis sets of all self-orthogonal, self-dual and complementary-dual negacyclic additive codes of length [Formula: see text] over [Formula: see text] when [Formula: see text] and enumerate these three class of codes for any integer [Formula: see text] with respect to the aforementioned trace bilinear forms on [Formula: see text]