Corrigendum to New Generalized Cyclotomic Binary Sequences of Period $p^2$

TL;DR

This paper introduces new generalized cyclotomic binary sequences of period p^2, analyzes their properties, and demonstrates they have high linear complexity for non-Wieferich primes, enhancing sequence design for cryptography.

Contribution

It proposes a new class of sequences of period p^2 and determines their linear complexity, especially for non-Wieferich primes, which was not previously known.

Findings

Sequences are almost balanced.

Linear complexity is very large for non-Wieferich primes.

Sequences are suitable for cryptographic applications.

Abstract

New generalized cyclotomic binary sequences of period $p^2$ are proposed in this paper, where $p$ is an odd prime. The sequences are almost balanced and their linear complexity is determined. The result shows that the proposed sequences have very large linear complexity if $p$ is a non-Wieferich prime.