Bull. Korean Math. Soc. 2018; 55(2): 341-357
Online first article March 9, 2018 Printed March 30, 2018
https://doi.org/10.4134/BKMS.b160842
Copyright © The Korean Mathematical Society.
Steven T. Dougherty, Jon-Lark Kim, Nari Lee
University of Scranton, Sogang University, Sogang University
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
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