Linear complexity and trace representation of quaternary sequences over $\mathbb{Z}_4$ based on generalized cyclotomic classes modulo $pq$

TL;DR

This paper introduces a method to analyze quaternary sequences over our of length pq, using generalized cyclotomic classes, and computes their linear complexity and trace representation via DFT.

Contribution

It presents a novel approach to determine linear complexity and trace representation of sequences over our based on generalized cyclotomic classes modulo pq.

Findings

Exact values of linear complexity are obtained.

Trace representations of the sequences are explicitly derived.

DFT analysis reveals the spectral properties of the sequences.

Abstract

We define a family of quaternary sequences over the residue class ring modulo $4$ of length $pq$, a product of two distinct odd primes, using the generalized cyclotomic classes modulo $pq$ and calculate the discrete Fourier transform (DFT) of the sequences. The DFT helps us to determine the exact values of linear complexity and the trace representation of the sequences.