NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS

RÚA, IGNACIO F. 

Glasgow mathematical journal, Tome 62 (2020), pp. S186-S205

Résumé

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.

Détail

DOI : 10.1017/S0017089520000191

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