Generalized Fourier Transform and the Joint N-Adic Complexity of a Multisequence

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 S-1, S-2, ... , S-m 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.