Finite semifields: A brief history and current directions

2017 ◽  
Author(s):  
Gregory P. Wene
Keyword(s):  
Finite Semifields

scholarly journals A note on finite semifields and certain p-groups of class 2

2004 ◽  
Vol 275 (1-3) ◽  
pp. 355-362 ◽  
Author(s):  
N.R. Rocco ◽  
J.S. Rocha
Keyword(s):  
Finite Semifields

scholarly journals A survey of finite semifields

1999 ◽  
Vol 208-209 ◽  
pp. 125-137 ◽  
Author(s):  
M. Cordero ◽  
G.P. Wene
Keyword(s):  
Finite Semifields

scholarly journals Finite semifields and nonsingular tensors

2012 ◽  
Vol 68 (1-3) ◽  
pp. 205-227 ◽  
Author(s):  
Michel Lavrauw
Keyword(s):  
Finite Semifields

Some recent directions in finite semifields

2018 ◽  
Vol 27 (07) ◽  
pp. 1841014 ◽  
Author(s):  
Gregory P. Wene
Keyword(s):  
Detailed Examination ◽  
History Of ◽  
Finite Semifields ◽  
Fractional Dimensions

A brief history of finite semifields upto 1965 is followed by a more detailed examination of recent discoveries with particular emphasis on constructions, fractional dimensions and cyclic semifields. Other results are also developed.

scholarly journals NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS

2020 ◽  
Vol 62 (S1) ◽  
pp. S186-S205 ◽  
Author(s):  
IGNACIO F. RÚA
Keyword(s):  
Galois Field ◽  
Binary Codes ◽  
Kerdock Codes ◽  
Finite Semifields ◽  
Goethals Codes

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.

scholarly journals Segre embeddings and finite semifields

2014 ◽  
Vol 25 ◽  
pp. 8-18 ◽  
Author(s):  
Michel Lavrauw ◽  
Corrado Zanella
Keyword(s):  
Finite Semifields
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