Planar Functions and Planes of Lenz-Barlotti Class II
Designs, Codes and Cryptography
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Some Theorems on Planar Mappings
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
New Perfect Nonlinear Multinomials over F$_{p^{2k}}$ for Any Odd Prime p
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
New Commutative Semifields and Their Nuclei
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
New semifields, PN and APN functions
Designs, Codes and Cryptography
Switching construction of planar functions on finite fields
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Commutative semifields from projection mappings
Designs, Codes and Cryptography
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We consider the implications of the equivalence of commutative semifields of odd order and planar Dembowski-Ostrom polynomials. This equivalence was outlined recently by Coulter and Henderson. In particular, following a more general statement concerning semifields we identify a form of planar Dembowski-Ostrom polynomial which must define a commutative semifield with the nuclei specified. Since any strong isotopy class of commutative semifields must contain at least one example of a commutative semifield described by such a planar polynomial, to classify commutative semifields it is enough to classify planar Dembowski-Ostrom polynomials of this form and determine when they describe non-isotopic commutative semifields. We prove several results along these lines. We end by introducing a new commutative semifield of order 38 with left nucleus of order 3 and middle nucleus of order 32.