M-Ary Character-Based Sequences of Length pq With Low Autocorrelation
Andrzej K. Brodzik, Richard Tolimieri · IEEE Transactions on Information Theory · 2022
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$6 mid M$, 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.