Planar difference functions
Planar difference functions
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, $x^3$ is the only Alltop type function.
Accepted to ISIT2012. v2 added a reference and adjusted margins
- University of Queensland Australia
- RMIT University Australia
- University of Queensland Australia
- Charles University Czech Republic
- Queensland University of Technology Australia
FOS: Computer and information sciences, cubic phase sequencs, Quantum Physics, polynomials, Computer Science - Information Theory, Information Theory (cs.IT), FOS: Physical sciences, welch bound, FOS: Mathematics, Mathematics - Combinatorics, quantum cryptography, Combinatorics (math.CO), Quantum Physics (quant-ph)
FOS: Computer and information sciences, cubic phase sequencs, Quantum Physics, polynomials, Computer Science - Information Theory, Information Theory (cs.IT), FOS: Physical sciences, welch bound, FOS: Mathematics, Mathematics - Combinatorics, quantum cryptography, Combinatorics (math.CO), Quantum Physics (quant-ph)
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