On the Galois dual of one-generator quasi-monomial codes

In this paper, we study 1-generator quasi-monomial (QM) codes over finite fields, where we describe the Galois dual codes of 1-generator QM codes of index 2. We show that 1-generator QM codes are Galois self-orthogonal under certain conditions. We investigate certain maximum distance separable quantum codes (quantum MDS codes) and certain almost maximum distance separable quantum codes (quantum AMDS codes). Moreover, we present many examples of quantum codes with good parameters, including new MDS and AMDS codes over various finite fields.