On the linear complexity of new generalized cyclotomic binary sequences of period p n q m

V A Edemskiy,S V Garbar

doi:10.1088/1742-6596/1658/1/012009

Abstract

Sequences with high linear complexity are of importance in different applications. These sequences can be derived from generalized cyclotomic classes. In this paper, we construct new families of binary sequences of period p n q m using new generalized cyclotomic classes, as well as study the linear complexity of these sequences. We obtain the estimate of the linear complexity of new sequences and show that they have high linear complexity for m + n > 2.

Highlights

The cyclotomic classes and the generalized cyclotomic classes are often used for design sequences with high linear complexity, which is an important characteristic of sequence for the cryptography applications [2]
A new family of binary sequences with period 2pn based on the generalized cyclotomic classes from [8] was presented in [6]
Yi Ouang et al examined the linear complexity of these sequences for f = 2r, where p = 1 + e f and r is a positive integer

Summary

Introduction

The cyclotomic classes and the generalized cyclotomic classes are often used for design sequences with high linear complexity, which is an important characteristic of sequence for the cryptography applications [2]. A new family of binary sequences with period 2pn based on the generalized cyclotomic classes from [8] was presented in [6]. In this paper we show that for study of the linear complexity of new sequence family from [6] we can use only old the method from [4]. It will be enough for obtaining more generalized results than in [6] and for the proof and the correction of the conjecture of the authors of this paper.

Preliminaries

Linear Complexity

New Generalized Cyclotomic Sequences Length 2pn

Main Result

Findings

Additional remark