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. [ABSTRACT FROM AUTHOR]