Linear complexity and trace representation of quaternary sequences over $\mathbb{Z}_4$ based on generalized cyclotomic classes modulo $pq$
This work addresses cryptographic sequence design for secure communications, but it is incremental as it builds on existing cyclotomic methods.
The authors tackled the problem of constructing quaternary sequences over Z4 with good cryptographic properties by defining a family based on generalized cyclotomic classes modulo pq, and they derived exact values for linear complexity and trace representation using discrete Fourier transform.
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.