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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