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 root 5 or 3, (2) we show that the smallest maximum autocorrelation sidelobe magnitude of an M-ary character-based sequence, when 4 inverted iota;M, either decreases with M and tends to 2, when 6 (sic) M, or is equal to 2, when 6 inverted iota 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 root 3, and, in particular, is equal to root 3 for the sextic phase sequence.