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

作者：Hall Joanne L^*; Rao Asha; Gagola Stephen M III

来源：IEEE Transactions on Communications, 2013, 61(11): 4722-4727.

DOI：10.1109/TCOMM.2013.091813.130127

• Planar function
• Alltop function
• mutually unbiased bases
• MUBs
• CDMA

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.

• 出版日期2013-11