A Family of Alltop Functions that are EA-Inequivalent to the Cubic Function

Author

Hall, Joanne L. ; Rao, Asha ; Gagola, Stephen M.

Author_Institution

Queensland University of Technology. This research was done while she was with the Department of Algebra, Charles University, Prague, Czech Republic

Volume

61

Issue

11

fYear

2013

fDate

Nov-13

Firstpage

4722

Lastpage

4727

Abstract

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (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 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.

Keywords

Additives; Correlation; Educational institutions; Multiaccess communication; Polynomials; Vectors; Alltop function; CDMA; MUBs; Planar function; mutually unbiased bases;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOMM.2013.091813.130127

Filename

6612625