New Commutative Semifields and Their Nuclei

Abstract. Commutative semifields in odd characteristic can be equivalently described by planar functions (also known as PN functions). We describe a method to construct a semifield which is canonically associated to a planar function and use it to derive information on the nuclei directly from the planar function. This is used to determine the nuclei of families of new commutative semifields of dimensions 9 and 12 in arbitrary odd characteristic. Key Words: PN functions, planar functions, presemifields, semifields, middle nucleus, kernel, Dembowski-Ostrom polynomial, isotopy, strong isotopy

• Type: Conference
• Year: 2009
• Where: AAECC
• Authors: Jürgen Bierbrauer
• Keywords: AAECC 2009, Algorithms, Odd Characteristic, Planar Functions, PN Functions