Autocorrelation of a class of quaternary sequences of period 2pm2p^m

Sequences with good randomness properties are quite important for stream ciphers. In this paper, a new class of quaternary sequences is constructed by using generalized cyclotomic classes of $\mathbb{Z}_{2p^m}$ $(m\geq1)$. The exact values of autocorrelation of these sequences are determined based on cyclotomic numbers of order $2$ with respect to $p^m$. Results show that the presented sequences have the autocorrelations with at most $4$ values

Linear Complexity of a Family of Pseudorandom Discrete Logarithm Threshold Sequences

Abstract We discuss the linear complexity of a family of binary threshold sequence defined by the discrete logarithm of integers modulo a large prime. It is proved that the linear complexity is at least the half of their period and under some special conditions the linear complexity can achieve maximal