The merit factor problem asks for binary sequences with small off-zero correlations. Let 
be the set of sequences 
with 
and 
for 
, ..., 
, and define
for 
,
1, ..., 
.
Then the merit factor problem requires the minimization of 
over 
for a fixed positive integer 
.
For 
,
2, ..., the first few minima are 5, 10, 18, 27, 43, 52, 72, ... (OEIS A091386).
Finding optimal sequences is computationally difficult (Borwein and Bailey 2003, p. 6).
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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
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