Geodesic
NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS
Glasgow mathematical journal, Tome 62 (2020), pp. S186-S205

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DOI

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. 
RÚA, IGNACIO F. NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS. Glasgow mathematical journal, Tome 62 (2020), pp. S186-S205. doi: 10.1017/S0017089520000191
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     author = {R\'UA, IGNACIO F.},
     title = {NONBINARY {DELSARTE{\textendash}GOETHALS} {CODES} {AND} {FINITE} {SEMIFIELDS}},
     journal = {Glasgow mathematical journal},
     pages = {S186--S205},
     year = {2020},
     volume = {62},
     number = {S1},
     doi = {10.1017/S0017089520000191},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000191/}
}
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