NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS
2020 ◽
Vol 62
(S1)
◽
pp. S186-S205
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AbstractSymplectic 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.
1998 ◽
Vol 52
(10)
◽
pp. 1485-1493
Keyword(s):
2009 ◽
Vol 116
(2)
◽
pp. 434-448
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Keyword(s):
2008 ◽
Vol 54
(4)
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pp. 1760-1765
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