M-Ary Character-Based Sequences of Length pq With Low Autocorrelation

Using elementary properties of primitive multiplicative characters we derive the autocorrelation of a unimodular
$M$
-ary character-based sequence of length
$pq$
, where
$p$
and
$q$
are distinct odd primes. Subsequently: (1) we identify three new sets of twin-prime quadriphase sequences with the largest autocorrelation sidelobe magnitude equal to
$\sqrt {5}$
or 3, (2) we show that the smallest maximum autocorrelation sidelobe magnitude of an
$M$
-ary character-based sequence, when
$4|M$
, either decreases with
$M$
and tends to 2, when
$6\nmid M$
, or is equal to 2, when
$6|M$
, and (3), we show that the smallest maximum autocorrelation sidelobe magnitude of a full-alphabet
$M$
-ary character-based sequence, where
$M>2$
, is greater or equal to
$\sqrt {3}$
, and, in particular, is equal to
$\sqrt {3}$
for the sextic phase sequence.