• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.297-310
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• 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.341-357
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• 2018

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 ${\mathbb{F}}_{2^{2s}}$ 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.