goethals codes
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2020 ◽  
Vol 62 (S1) ◽  
pp. S186-S205 ◽  
Author(s):  
IGNACIO F. RÚA

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.


2014 ◽  
Vol 40 (2) ◽  
pp. 601-631
Author(s):  
Sihuang Hu ◽  
Tao Feng ◽  
Gennian Ge

2001 ◽  
Vol 25 (2) ◽  
pp. 257-268
Author(s):  
Cui Jie ◽  
Zhexian Wan
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