Recently the word-based stream ciphers have been the subject of a considerable amount of research. The theory of such stream ciphers requires the study of the complexity of a multisequence. Let S1, S2, . . . , Sm be m N-ary sequences of period T, i.e., a multisequence. The relationship between the joint N-adic complexity and the number of the nonzero columns of the generalized Fourier transform for the N-ary multisequence is determined which generalizes the well-known result about the joint linear complexity and the generalized Fourier transform for a multisequence to the case of the joint N-adic complexity.

The stability theory of stream ciphers plays an important role in designing good stream cipher systems. Two algorithms are presented, to determine the optimal shift and the minimum linear complexity of the sequence, that differs from a given sequence over Fq with period qn-1 by one digit. We also describe how the linear complexity changes with respect to one digit differing from a given sequence.

In this paper, new classes of binary generalized cyclotomic sequences of period 2pm+1qn+1 are constructed. These sequences are balanced. We calculate the linear complexity of the constructed sequences with a simple method. The results show that the linear complexity of such sequences attains the maximum.