3 research outputs found
Linear complexity of quaternary sequences over Z4 based on Ding-Helleseth generalized cyclotomic classes
A family of quaternary sequences over Z4 is defined based on the
Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd
primes p and q. The linear complexity is determined by computing the defining
polynomial of the sequences, which is in fact connected with the discrete
Fourier transform of the sequences. The results show that the sequences possess
large linear complexity and are good sequences from the viewpoint of
cryptography
Linear complexity and trace representation of quaternary sequences over based on generalized cyclotomic classes modulo
We define a family of quaternary sequences over the residue class ring modulo
of length , a product of two distinct odd primes, using the generalized
cyclotomic classes modulo 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.Comment: 16 page
Linear complexity of quaternary sequences over Z_4 derived from generalized cyclotomic classes modulo 2p
We determine the exact values of the linear complexity of 2p-periodic
quaternary sequences over Z_4 (the residue class ring modulo 4) defined from
the generalized cyclotomic classes modulo 2p in terms of the theory of of
Galois rings of characteristic 4, where p is an odd prime. Compared to the case
of quaternary sequences over the finite field of order 4, it is more dificult
and complicated to consider the roots of polynomials in Z_4[X] due to the zero
divisors in Z_4 and hence brings some interesting twists. We answer an open
problem proposed by Kim, Hong and Song