The Shift-and-Add Property of m-Sequences

Regular Section

Fanxin ZENG, Lijia GE, Xiping HE, College of Communication Engineering, Chongqing University">Guixin XUAN, Guojun LI, Zhenyu ZHANG, Yanni PENG, Linjie QIAN, Sheng LU

Author information

Fanxin ZENG
Chongqing Engineering Laboratory for Detection, Control and Integrated System, Chongqing Technology and Business University
Lijia GE
Communication NCO Academy, Army Engineering University of PLA
Xiping HE
Chongqing Engineering Laboratory for Detection, Control and Integrated System, Chongqing Technology and Business University
Guixin XUAN
Communication NCO Academy, Army Engineering University of PLA
College of Communication Engineering, Chongqing University
Guojun LI
College of Photoelectric Engineering, Chongqing University of Posts and Telecommunications
Zhenyu ZHANG
Communication NCO Academy, Army Engineering University of PLA
Yanni PENG
Chongqing Engineering Laboratory for Detection, Control and Integrated System, Chongqing Technology and Business University
Linjie QIAN
Communication NCO Academy, Army Engineering University of PLA
Sheng LU
Chongqing Engineering Laboratory for Detection, Control and Integrated System, Chongqing Technology and Business University

Keywords: shift-and-add property, m-sequences, trinomial, reciprocal polynomial, cyclotomic cosets

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2019 Volume E102.A Issue 4 Pages 685-690

DOI https://doi.org/10.1587/transfun.E102.A.685

Details

Abstract

The shift-and-add property (SAP) of a p-ary m-sequence {a_k} with period N=pⁿ-1 means that this sequence satisfies the equation {a_k+η}+{a_k+τ}={a_k+λ} for some integers η, τ and λ. For an arbitrarily-given p-ary m-sequence {a_k}, we develop an algebraic approach to determine the integer λ for the arbitrarily-given integers η and τ. And all trinomials can be given. Our calculation only depends on the reciprocal polynomial of the primitive polynomial which produces the given m-sequence {a_k}, and the cyclotomic cosets mod pⁿ-1.

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