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.
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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|Item Type:||Conference Paper|
|Keywords:||polynomials, welch bound, cubic phase sequencs, quantum cryptography|
|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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