Commutative semifields from projection mappings

We describe a general projection method to construct commutative semifields in odd characteristic. One application yields a family of commutative semifields of order q 2 m with middle nucleus of order at least q 2 for every odd prime-power q and every odd integer m  > 1. Another application of th...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2011-11, Vol.61 (2), p.187-196
Main Author: Bierbrauer, Jürgen
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
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Summary:We describe a general projection method to construct commutative semifields in odd characteristic. One application yields a family of commutative semifields of order q 2 m with middle nucleus of order at least q 2 for every odd prime-power q and every odd integer m  > 1. Another application of the method yields a generalization of the Budaghyan–Helleseth family and also greatly simplifies the construction.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-010-9447-z