NDLI: Planar polynomials for commutative semifields with specified nuclei

Content Provider	Springer Nature Link
Author	Coulter, Robert S. Henderson, Marie Kosick, Pamela
Copyright Year	2007
Abstract	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.
Starting Page	275
Ending Page	286
Page Count	12
File Format	PDF
ISSN	09251022
Journal	Designs, Codes and Cryptography
Volume Number	44
Issue Number	1-3
e-ISSN	15737586
Language	English
Publisher	Springer US
Publisher Date	2007-08-02
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Commutative semifields Nuclei Planar polynomials Information and Communication, Circuits Discrete Mathematics in Computer Science Data Encryption Data Structures, Cryptology and Information Theory Coding and Information Theory Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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