Nonbinary sequences with perfect and nearly perfect autocorrelations

On the relative abundance of nonbinary sequences with perfect autocorrelations

“…For example, Ω + 2 = {0, −1, 1} is the ternary alphabet and Ω + 4 = {0, ±1, ± √ −1} is the alphabet we call QP SK + . We recall a construction discussed by Boztaş and Udaya in [2]: Definition 3. Let m ≡ −2 (mod q) and let the maximal length sequence of period L = q m − 1 over F q be given by…”

Nearly perfect Gaussian integer sequences with arbitrary degree

“…Compared with traditional sequences, elements with equal magnitude are not desired in Gaussian integer sequences. Recently, perfect Gaussian integer sequences (PGISs) have been investigated in the literature [10][11][12][13][14][15][16][17][18][19][20][21][22]. Hu et al [10] presented PGISs of even period by linearly combining base sequences or their shift equivalents.…”

Distinct 8-QAM+ Perfect Arrays

“…There are a large number of perfect binary, ternary, and ployphase array [1]. However, 8-QAM+ perfect arrays are rare, whose main reason lies at the late introduction of 8-QAM+ constellation [2]. In 2010, Boztas and Parampalli introduced the definition of 8-QAM+ signal set [2].…”

“…However, 8-QAM+ perfect arrays are rare, whose main reason lies at the late introduction of 8-QAM+ constellation [2]. In 2010, Boztas and Parampalli introduced the definition of 8-QAM+ signal set [2]. From that time on, the sequences over 8-QAM+ constellation are rapidly developed.…”