A family of Alltop functions that are EA-inequivalent to the cubic function

Hall, Joanne L., Rao, Asha, & Gagola, Stephen M. (2013) A family of Alltop functions that are EA-inequivalent to the cubic function. IEEE Transactions on Communications, 61(11), pp. 4722-4727.

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Abstract

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (\emph{IEEE Trans. Inf. Theory} 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these sequences were optimal with respect to the known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases (MUBs), a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called \emph{Alltop functions}. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs.

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ID Code: 62316
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Planar function, Alltop function, mutually unbiased bases, MUBs, CDMA
DOI: 10.1109/TCOMM.2013.091813.130127
ISSN: 0090-6778
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 > MATHEMATICAL SCIENCES (010000) > MATHEMATICAL PHYSICS (010500) > Algebraic Structures in Mathematical Physics (010501)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > ELECTRICAL AND ELECTRONIC ENGINEERING (090600) > Electrical and Electronic Engineering not elsewhere classified (090699)
Divisions: Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 IEEE
Copyright Statement: Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Deposited On: 05 Sep 2013 22:37
Last Modified: 23 Jan 2014 16:48

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