Details

Autor(en) / Beteiligte

• Brodzik, Andrzej K.
• Tolimieri, Richard

Titel

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

Ist Teil von

• IEEE transactions on information theory, 2022-09, Vol.68 (9), p.6207-6217

Ort / Verlag

IEEE

Erscheinungsjahr

2022

Link zum Volltext

• IEEE_Xplore

Quelle

IEEE Electronic Library (IEL)

Beschreibungen/Notizen

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