Additive G-codes over Fq and their dualities

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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.

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Dougherty, S. T., & Fernández-Córdoba, C. (2021). Additive G-codes over Fq and their dualities. Finite Fields and Their Applications, 72.

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