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Paper Title The F_M-linear Complexity of M-ary Sidel’nikov Sequences of Period p−1 = f ·M^λ
Paper IdentifierTH3.R9.3
Authors Min Zeng, Yuan Luo, Shanghai Jiao Tong University, China; Min-Kyu Song, Hong-Yeop Song, Yonsei University, Korea (South)
Session Sequences
Location Pontoise, Level 5
Session Time Thursday, 11 July, 14:30 - 16:10
Presentation Time Thursday, 11 July, 15:10 - 15:30
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Abstract 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 F_M -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 F_3 -linear complexities of the 3-ary Sidel’nikov sequences are determined for p = 2 · 3^ λ + 1(1 ≤λ ≤ 20). It turns out that all of the linear complexities of the considered sequences are very close to their periods.