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NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS
Published online by Cambridge University Press: 07 May 2020
Abstract
Symplectic finite semifields can be used to construct nonlinear binary codes of Kerdock type (i.e., with the same parameters of the Kerdock codes, a subclass of Delsarte–Goethals codes). In this paper, we introduce nonbinary Delsarte–Goethals codes of parameters
$(q^{m+1}\ ,\ q^{m(r+2)+2}\ ,\ {\frac{q-1}{q}(q^{m+1}-q^{\frac{m+1}{2}+r})})$
over a Galois field of order
$q=2^l$
, for all
$0\le r\le\frac{m-1}{2}$
, with m ≥ 3 odd, and show the connection of this construction to finite semifields.
MSC classification
- Type
- Research Article
- Information
- Glasgow Mathematical Journal , Volume 62 , Special Issue S1: Workshop on Nonassociative algebras and their applications , December 2020 , pp. S186 - S205
- Copyright
- © The Author(s) 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust
References
REFERENCES
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