We define additive G-codes over finite fields. We prove that if C is an additive G-code over Fq with duality M then its dual with respect to this duality CM is an additive G-code. We prove that if M and M′ are two dualities, then CM and CM′ are equivalent codes. Finally, we study the existence of self-dual codes for a variety of dualities and relate them to formally self-dual and linear self-dual codes.
Dougherty, S. T., & Fernández-Córdoba, C. (2021). Additive G-codes over Fq and their dualities. Finite Fields and Their Applications, 72. https://doi.org/10.1016/j.ffa.2021.101821