Abstract
We study self-dual codes over non-commutative Frobenius rings. It is shown that a code is equal to its left orthogonal if and only if it is equal to its right orthogonal. Constructions of self-dual codes are given over Frobenius rings that arise from self-dual codes over the center of the ring. These constructions are used to show for which lengths self-dual codes exist over various rings.
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The author is grateful to the Université d’Artois where he stayed while this work was completed.
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Dougherty, S.T., Leroy, A. Euclidean self-dual codes over non-commutative Frobenius rings. AAECC 27, 185–203 (2016). https://doi.org/10.1007/s00200-015-0277-0
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DOI: https://doi.org/10.1007/s00200-015-0277-0