IEICE TRANSACTIONS on Fundamentals
Linear Complexity of Pseudorandom Sequences Derived from Polynomial Quotients: General Cases
Summary :
We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by $F(u)equiv rac{f(u)-f_p(u)}{p} ~(mod~ p), qquad 0 le F(u) le p-1,~uge 0,$ where fp(u)≡f(u) (mod p), for general polynomials $f(x)in mathbb{Z}[x]$. The linear complexity equals to one of the following values {p2-p,p2-p+1,p2-1,p2} if 2 is a primitive root modulo p2, depending on p≡1 or 3 modulo 4 and the number of solutions of f'(u)≡0 (mod) p, where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d|(p-1) and d being a primitive root modulo p2.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.4 pp.970-974
- Publication Date
- 2014/04/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.970
- Type of Manuscript
- PAPER
- Category
- Information Theory
Authors
Xiaoni DU
Northwest Normal Univ.,Xidian Univ.
Ji ZHANG
Northwest Normal Univ.,Xidian Univ.
Chenhuang WU
Putian University
Keyword
Latest Issue
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Xiaoni DU, Ji ZHANG, Chenhuang WU, "Linear Complexity of Pseudorandom Sequences Derived from Polynomial Quotients: General Cases" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 4, pp. 970-974, April 2014, doi: 10.1587/transfun.E97.A.970.
Abstract: We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by $F(u)equiv rac{f(u)-f_p(u)}{p} ~(mod~ p), qquad 0 le F(u) le p-1,~uge 0,$ where fp(u)≡f(u) (mod p), for general polynomials $f(x)in mathbb{Z}[x]$. The linear complexity equals to one of the following values {p2-p,p2-p+1,p2-1,p2} if 2 is a primitive root modulo p2, depending on p≡1 or 3 modulo 4 and the number of solutions of f'(u)≡0 (mod) p, where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d|(p-1) and d being a primitive root modulo p2.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.970/_p
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@ARTICLE{e97-a_4_970,
author={Xiaoni DU, Ji ZHANG, Chenhuang WU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Linear Complexity of Pseudorandom Sequences Derived from Polynomial Quotients: General Cases},
year={2014},
volume={E97-A},
number={4},
pages={970-974},
abstract={We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by $F(u)equiv rac{f(u)-f_p(u)}{p} ~(mod~ p), qquad 0 le F(u) le p-1,~uge 0,$ where fp(u)≡f(u) (mod p), for general polynomials $f(x)in mathbb{Z}[x]$. The linear complexity equals to one of the following values {p2-p,p2-p+1,p2-1,p2} if 2 is a primitive root modulo p2, depending on p≡1 or 3 modulo 4 and the number of solutions of f'(u)≡0 (mod) p, where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d|(p-1) and d being a primitive root modulo p2.},
keywords={},
doi={10.1587/transfun.E97.A.970},
ISSN={1745-1337},
month={April},}
Copy
TY - JOUR
TI - Linear Complexity of Pseudorandom Sequences Derived from Polynomial Quotients: General Cases
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 970
EP - 974
AU - Xiaoni DU
AU - Ji ZHANG
AU - Chenhuang WU
PY - 2014
DO - 10.1587/transfun.E97.A.970
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2014
AB - We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by $F(u)equiv rac{f(u)-f_p(u)}{p} ~(mod~ p), qquad 0 le F(u) le p-1,~uge 0,$ where fp(u)≡f(u) (mod p), for general polynomials $f(x)in mathbb{Z}[x]$. The linear complexity equals to one of the following values {p2-p,p2-p+1,p2-1,p2} if 2 is a primitive root modulo p2, depending on p≡1 or 3 modulo 4 and the number of solutions of f'(u)≡0 (mod) p, where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d|(p-1) and d being a primitive root modulo p2.
ER -
English
