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arXiv · 1302.4498

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

Joanne L. Hall·Asha Rao·Stephen M. Gagola III
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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.

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Joanne L. Hall, Asha Rao, Stephen M. Gagola III. 2013-02-19. A family of Alltop functions that are EA-inequivalent to the cubic function. https://doi.org/10.1109/tcomm.2013.091813.130127

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