Planar Difference Functions
Combinatorics
2012-07-31 v2 Information Theory
math.IT
Quantum Physics
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, is the only Alltop type function.
Cite
@article{arxiv.1205.3310,
title = {Planar Difference Functions},
author = {Joanne L. Hall and Asha Rao and Diane Donovan},
journal= {arXiv preprint arXiv:1205.3310},
year = {2012}
}
Comments
Accepted to ISIT2012. v2 added a reference and adjusted margins