Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field

Abstract

We provide a sequence with high nonlinear complexity from the Hermitian function field H over F q 2 . This sequence was obtained using a rational function with pole divisor in certain collinear rational places on H, where 2 ≤ ≤ q. In particular we improve the lower bounds on the kth-order nonlinear complexity obtained by H. Niederreiter and C. Xing [12]; and O. Geil, F. Özbudak and D. Ruano [5].

Binary sequences with length n and nonlinear complexity not less than n/2

“…By applying a combinatorial method, all m-ary sequences of length n and nonlinear complexity n − j, where 2 ≤ j ≤ 4 and n ≥ 2j, were characterized in [18,25]. In addition, several constructions of finite-length sequences with large nonlinear complexity profile from function fields were studied in [2,14,17].…”