The Shift-and-Add Property of m-Sequences

Fanxin ZENG; Lijia GE; Xiping HE; Guixin XUAN; Guojun LI; Zhenyu ZHANG; Yanni PENG; Linjie QIAN; Sheng LU

doi:10.1587/transfun.E102.A.685

The Shift-and-Add Property of m-Sequences

Fanxin ZENG, Lijia GE, Xiping HE, Guixin XUAN, Guojun LI, Zhenyu ZHANG, Yanni PENG, Linjie QIAN, Sheng LU

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.4 pp.685-690

Publication Date: 2019/04/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E102.A.685

Type of Manuscript: LETTER

Category: Information Theory

Authors

Fanxin ZENG
  Chongqing Technology and Business University
Lijia GE
  Army Engineering University of PLA
Xiping HE
  Chongqing Technology and Business University
Guixin XUAN
  Army Engineering University of PLA,Chongqing University
Guojun LI
  Chongqing University of Posts and Telecommunications
Zhenyu ZHANG
  Army Engineering University of PLA
Yanni PENG
  Chongqing Technology and Business University
Linjie QIAN
  Army Engineering University of PLA
Sheng LU
  Chongqing Technology and Business University

Keyword

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

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Fanxin ZENG, Lijia GE, Xiping HE, Guixin XUAN, Guojun LI, Zhenyu ZHANG, Yanni PENG, Linjie QIAN, Sheng LU, "The Shift-and-Add Property of m-Sequences" in IEICE TRANSACTIONS on Fundamentals, vol. E102-A, no. 4, pp. 685-690, April 2019, doi: 10.1587/transfun.E102.A.685.
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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.685/_p

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@ARTICLE{e102-a_4_685,
author={Fanxin ZENG, Lijia GE, Xiping HE, Guixin XUAN, Guojun LI, Zhenyu ZHANG, Yanni PENG, Linjie QIAN, Sheng LU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Shift-and-Add Property of m-Sequences},
year={2019},
volume={E102-A},
number={4},
pages={685-690},
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.},
keywords={},
doi={10.1587/transfun.E102.A.685},
ISSN={1745-1337},
month={April},}

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TY - JOUR
TI - The Shift-and-Add Property of m-Sequences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 685
EP - 690
AU - Fanxin ZENG
AU - Lijia GE
AU - Xiping HE
AU - Guixin XUAN
AU - Guojun LI
AU - Zhenyu ZHANG
AU - Yanni PENG
AU - Linjie QIAN
AU - Sheng LU
PY - 2019
DO - 10.1587/transfun.E102.A.685
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2019
AB - 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.
ER -