Linear complexity problems of level sequences of Euler quotients and their related binary sequences

The Euler quotient modulo an odd-prime power pr （r 〉 1） can be uniquely decomposed as a p-adic number of the form （u（p- 1）Pr- 1 _ 1）/pr ≡- ao （u） ＋ a1 （u）p ＋... ＋at- 1 （u）Pr- 1 （mod pr）, gcd（u, p） = 1, where 0 ≤ aj（u） 〈 p for 0 ≤ j≤r - 1 and we set all aj（u） = 0 if gcd（u,p） 〉 1. We firstly study cer...

Full description

Saved in:
Bibliographic Details
Published in:Science China. Information sciences 2016-03, Vol.59 (3), p.71-82, Article 32106
Main Authors: Niu, Zhihua, Chen, Zhixiong, Du, Xiaoni
Format: Article
Language:English
Subjects:
CDH
CL-AKA
Complexity
Computer Science
Information Systems and Communication Service
Quotients
Research Paper
信息科学
科学
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Euler quotient modulo an odd-prime power pr （r 〉 1） can be uniquely decomposed as a p-adic number of the form （u（p- 1）Pr- 1 _ 1）/pr ≡- ao （u） ＋ a1 （u）p ＋... ＋at- 1 （u）Pr- 1 （mod pr）, gcd（u, p） = 1, where 0 ≤ aj（u） 〈 p for 0 ≤ j≤r - 1 and we set all aj（u） = 0 if gcd（u,p） 〉 1. We firstly study certain arithmetic properties of the level sequences （aj（u））u≥0 over Fp via introducing a new quotient. Then we determine the exact values of linear complexity of （aj（u））u≥0 and values of k-error linear complexity for binary sequences defined by （aj （U））u≥0.
ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-015-5305-y