Bulletin of the
Korean Mathematical Society BKMS

We examine various dualities over the fields of even orders, giving new dualities for additive codes. We relate the MacWilliams relations and the duals of $\FF_{2^{2s}}$ codes for these various dualities. We study self-dual codes with respect to these dualities and prove that any subgroup of order $2^s$ of the additive group is a self-dual code with respect to some duality.

Keywords: additive codes, Hermitian inner-product, trace inner-product, self-dual codes

MSC numbers: Primary 11T71, 94B05