TOPICS

Merit Factor Problem

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook

Let A_n be the set of all sequences that contain all sequences {a_k}_(k=0)^n where a_0=1 and all other a_i=+/-1, and define

c_k=sum_(j=0)^(n-k)a_ja_(j+k).

Then the merit factor problem requires the minimization of sum_(k=0)^(n)c_k^2 over A_n for a fixed n.

For n=1, 2, ..., the first few minima are 5, 10, 18, 27, 43, 52, 72, ... (OEIS A091386).

This problem is known to be very hard, but is not known to be in one of the recognized combinatorial classes like NP (Borwein and Bailey 2003, p. 6).

Explore with Wolfram|Alpha

References

Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, 2003.Borwein, P. B. Computational Excursions in Analysis and Number Theory. New York: Springer-Verlag, 2002.Sloane, N. J. A. Sequence A091386 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Merit Factor Problem

Cite this as:

Weisstein, Eric W. "Merit Factor Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MeritFactorProblem.html

Subject classifications