Planar difference functions

Hall, Joanne L., Rao, Asha, & Donovan, Diane (2012) Planar difference functions. In 2012 IEEE International Symposium on Information Theory Proceedings (ISIT), IEEE Information Theory Society, Massachusetts Institute of Technology, Boston, MA, 1082 -1086.

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Abstract

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.

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ID Code: 58332
Item Type: Conference Paper
Refereed: Yes
Keywords: polynomials, welch bound, cubic phase sequencs, quantum cryptography
DOI: 10.1109/ISIT.2012.6283019
ISBN: 9781467325806
ISSN: 2157-8095
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Algebra and Number Theory (010101)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > DATA FORMAT (080400) > Coding and Information Theory (080401)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 IEEE
Copyright Statement: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
Deposited On: 18 Mar 2013 03:47
Last Modified: 04 Apr 2013 03:20

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