Tang et al. and Lim et al. presented ways to construct balanced quaternary sequences with even period and optimal autocorrelation value by inverse Gray-mapping of binary sequences with optimal autocorrelation value. In this article, we consider quaternary sequences constructed from binary Legendre or Hall’s sextic sequence by these methods. We derive the… (More)
Extended Abstract 1 Introduction.
—We examine the linear complexity and the autocor-relation of new quaternary cyclotomic sequences of period 2p. The sequences are constructed via the cyclotomic classes of order four.
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,… (More)
We found the linear complexity of generalized cyclotomic sequences with period $$2p^n$$ 2 p n based on quadratic, biquadratic and partially sextic residues. Our method is based on the generating the polynomial of the classical cyclotomic sequences, which allows us to obtain some well-known results and also some new results.
We defined sufficient conditions for designing Ding-Helleseth sequences with arbitrary period and high linear complexity for generalized cyclotomies. Also we discuss the method of computing the linear complexity of Ding-Helleseth sequences in the general case.