Search for Generalized MPS and Barker Sequences

The lowest achievable PSL for m
^th
-root-of-unity codes are found by several search approaches, including exhaustive search and an evolutionary algorithm, for lengths 2 ≤
$N$
≤ 15 and 2 ≤ m ≤ 20. Tabulation of the findings reveals patterns that may be used to inform searches for cases that remain un-resolved. Generalized Barker sequences were found for m = 6 for each
$N$
between 2 and 15, which implies that for these lengths, the same holds true when
$m$
is any multiple of 6. The findings suggest that generalized Barker sequences are not that rare, at least as far as cases N × m that harbor them.