Stephen M. Gagola III, Joanne L. Hall
Published 2013-02-14, updated 2016-03-01Version 2
The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We generalize this idea to a projection construction using two twisted semifields to construct semifields of odd characteristic. Planar functions and semifields have a strong connection so this also constructs new planar functions.
Regular $3$-polytopes of order $2^np$
Classification of 8-dimensional rank two commutative semifields
Planar functions and perfect nonlinear monomials over finite fields
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