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Indexed by:期刊论文

Date of Publication:2012-06-01

Journal:DESIGNS CODES AND CRYPTOGRAPHY

Included Journals:SCIE、EI

Volume:63

Issue:3

Page Number:413-423

ISSN No.:0925-1022

Key Words:Semifields; Planar functions; Difference sets

Abstract:It is proven that any Dembowski-Ostrom polynomial is planar if and only if its evaluation map is 2-to-1, which can be used to explain some known planar Dembowski-Ostrom polynomials. A direct connection between a planar Dembowski-Ostrom polynomial and a permutation polynomial is established if the corresponding semifield is of odd dimension over its nucleus. In addition, all commutative semifields of order 3(5) are classified.