Merit Factor Problem

Author

Eric W. Weisstein
January 11, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/MeritFactorProblem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MeritFactorProblem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

ASequences[n_]:=Prepend[#,1]&/@Flatten[Outer[List,Sequence@@Table[{-1,1},{n}]],n-1]

c[n_,k_]:=c[n,k]=Sum[a[j]a[j+k],{j,0,n-k}]

MeritFactor[l_]:=Sum[c[Length[l]-1,k]^2,{k,0,Length[l]-1}]/.a[i_]:>l[[i+1]]

Minima

ASequences[1]

{c[1,0],c[1,1]}

Min/@Table[MeritFactor/@ASequences[n],{n,15}]//Timing