Note on the Nonlinear Complexity of Finite Length Sequences

Recently, the nonlinear complexity of periodic binary sequences with a specific structure was investigated in [Yuan et al., IEEE Transactions on Information Theory 70(7), 5376–5391 (2024)], and a remaining problem is whether the maximum value of the nonlinear complexity of all right circular shifts of the sequence with length [Formula: see text] in the structure is [Formula: see text], where [Formula: see text] is the spacing between the maximum length identical subsequences with different successors. Based on the internal structure of the sequence, we verify that the maximum nonlinear complexity of all right cyclic shifts of [Formula: see text]-ary sequences with length [Formula: see text] equals [Formula: see text] when [Formula: see text].