Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2012-06-01

Journal: DESIGNS CODES AND CRYPTOGRAPHY

Included Journals: EI、SCIE

Volume: 63

Issue: 3

Page Number: 413-423

ISSN: 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.