Linear complexity of generalized cyclotomic sequences of period $2p^{m}$

TL;DR

This paper constructs two generalized cyclotomic binary sequences with period 2p^m and demonstrates that they possess high linear complexity for m ≥ 2, indicating their potential usefulness in cryptography.

Contribution

The paper introduces a new construction of generalized cyclotomic sequences of period 2p^m and analyzes their linear complexity, showing they are highly complex for m ≥ 2.

Findings

Sequences have high linear complexity for m ≥ 2

Construction based on generalized cyclotomy

Potential cryptographic applications

Abstract

In this paper, we construct two generalized cyclotomic binary sequences of period $2p^{m}$ based on the generalized cyclotomy and compute their linear complexity, showing that they are of high linear complexity when $m\geq 2$.