The F M -linear Complexity of M-ary Sidel’nikov Sequences of Period p − 1 = f • M λ
Min Zeng, Yuan Luo, Minkyu Song, Hong‐Yeop Song · 2019
The linear complexity is a measure for the unpredictability of a sequence over a finite field. Sequences with good pseudo-random properties and large linear complexity are widely used in the CDMA spread spectrum communication and cryptography. In recent years, many researchers have focused on the linear complexity of cyclotomic sequences such as Sidel'nikov sequence. This paper studies the FM-linear complexity of M-ary Sidel'nikov sequence of period p-1 using the Hasse derivative of its generating function, where M|(p-1). The tth Hasse derivative formulas are generalized in terms of cyclotomic numbers, and then the exact F3-linear complexities of the ternary Sidel'nikov sequences are determined for p = 2·3λ+1(1 ≤ λ ≤ 20). It turns out that all of the linear complexities of the considered sequences are very close to their periods.