Nonsingularity of Feedback Shift Registers of Degree at Most Three over a Finite Field

• 作者: LIU Junying JIANG Yupeng ZHENG Qunxiong LIN Dongdai
• 来源期刊: 电子学报（英文版）
• 年，卷（期）: 2021,（2）
• 所属期刊栏目: COMPUTERS AND MICROELECTRONICS
• 页码范围: 232-237
• 页数: 6页
• 语种: 英文
• DOI: 10.1049/cje.2021.01.009

摘要

As a kind of generators of pseudo-random sequences, the Feedback shift register (FSR) is widely used in channel coding, cryptography and digital communication. A necessary and sufficient condition for the nonsingularity of a feedback shift register of degree at most three over a finite field is established. Using the above result, we can easily determine the nonsingularity of a feedback shift register from the algebraic normal form of the corresponding feedback function.