A family of Alltop functions that are EA-inequivalent to the cubic function
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 functions were optimal with respect to known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases, 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.
Keywords
Cite
@article{arxiv.1302.4498,
title = {A family of Alltop functions that are EA-inequivalent to the cubic function},
author = {Joanne L. Hall and Asha Rao and Stephen M. Gagola},
journal= {arXiv preprint arXiv:1302.4498},
year = {2013}
}
Comments
15 pages