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Feifei YAN Pinhui KE Zuling CHANG
Recently, trace representation of a class of balanced quaternary sequences of period p from the classical cyclotomic classes was given by Yang et al. (Cryptogr. Commun.,15 (2023): 921-940). In this letter, based on the generalized cyclotomic classes, we define a class of balanced quaternary sequences of period pn, where p = ef + 1 is an odd prime number and satisfies e ≡ 0 (mod 4). Furthermore, we calculate the defining polynomial of these sequences and obtain the formula for determining their trace representations over ℤ4, by which the linear complexity of these sequences over ℤ4 can be determined.
Rayan MOHAMMED Xiaoni DU Wengang JIN Yanzhong SUN
We introduce the r-ary sequence with period 2p2 derived from Euler quotients modulo 2p (p is an odd prime) where r is an odd prime divisor of (p-1). Then based on the cyclotomic theory and the theory of trace function in finite fields, we give the trace representation of the proposed sequence by determining the corresponding defining polynomial. Our results will be help for the implementation and the pseudo-random properties analysis of the sequences.
Xina ZHANG Xiaoni DU Chenhuang WU
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.