On the 2-adic complexity and the κ-error 2-adic complexity of periodic binary sequences

被引：14

作者：

Hu, Honggang ^{[1
]}

Feng, Dengguo ^{[1
]}

机构：

[1] Chinese Acad Sci, Inst Software, State Key Lab Informat Secur, Beijing 100080, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2008年 / 54卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

2-adic complexity; expected value; k-error 2-adic complexity; k-error symmetric 2-adic complexity; l-sequence; periodic binary sequence; symmetric 2-adic complexity; variance;

D O I：

10.1109/TIT.2007.913238

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A significant difference between the linear complexity and the 2-adic complexity of periodic binary sequences is pointed out in this correspondence. Based on this observation, we present the concept of the symmetric 2-adic complexity of periodic binary sequences. The expected value of the 2-adic complexity is determined, and a lower bound on the expected value of the symmetric 2-adic complexity of periodic binary sequences is derived. We study the variance of the 2-adic complexity of periodic binary sequences, and the exact value for it is given. Because the 2-adic complexity of periodic binary sequences is unstable, we present the concepts of the k-error 2-adic complexity and the k-error symmetric 2-adic complexity, and lower bounds on them are also derived. In particular, we give tighter upper and lower bounds for the minimum 2-adic complexity of I-sequences by substituting two symbols within one period.

引用

页码：874 / 883

页数：10

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