Additive G-codes over Fq and their dualities

Abstract

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.