Remarks on a cyclotomic sequence

We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai et al. (IEEE Trans Inforem Theory 51: 1849-1853, 2005). First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider k-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this construction. The results show that the parameters for the sequence construction must be carefully chosen in view of the respective application

A general approach to construction and determination of the linear complexity of sequences based on cosets

We give a general approach to $N$-periodic sequences over a finite field \F_q constructed via a subgroup $D$ of the group of invertible elements modulo $N$. Well known examples are Legendre sequences or the two-prime generator. For some generalizations of sequences considered in the literature and for some new examples of sequence constructions we determine the linear complexity