Linear Complexity of Quaternary Sequences over Z4 Based on Ding-Helleseth Generalized Cyclotomic Classes

Xina ZHANG  Xiaoni DU  Chenhuang WU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.5   pp.867-871
Publication Date: 2018/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.867
Type of Manuscript: LETTER
Category: Information Theory
quaternary sequences,  Ding-Helleseth generalized cyclotomic classes,  defining polynomials,  linear complexity,  trace representation,  

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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.