Based on the use of Berlekamp-Massey algorithm, six conjectures for the linear complexity (LC) of some Kronecker sequences of two and three component codes are given. Components were chosen from the families of Gold, Kasami, Barker, Golay complementary and M-sequences. Typically, the LC value is a large part of the code length. The LC value of the outermost code influences mostly on the LC value.

Two classes of nonlinear feedforward logic (NLFFL) pseudonoise (PN) code generators based on the use of AND and majority logic (ML) gates are compared. Cross-correlation and code-division multiple-access (CDMA) properties of properly designed NLFFL sequences are found to be comparable with the properties of well-known linear PN codes. It is determined that code design employing ML gates with an odd number of inputs is easier compared with designing with AND gates. This is especially true when the degree of nonlinearity is large, since the nonbalance problem, e. g. , at the output of an AND gate, can be avoided. ML type sequences are less vulnerable to correlation attack and jamming by the m-sequence of an NLFFL generator

Two families of rapidly synchronizable spreading codes are compared using the same component codes. The influence of component code choice is also discussed. It is concluded that correlation, code-division multiple-access (CDMA) and information security (measured by the value of linear complexity) properties of Kronecker sequences are considerably better than those of Combination sequences. Combination sequences cannot be recommended for CDMA use unless the number of active users is few. CDMA performance of Kronecker sequences is almost comparable with that of linear pseudonoise (PN) code families of equal length when a Gold or Kasami code is used as the innermost code and the Barker code is used as the outermost code to guarantee satisfactory correlation and CDMA properties. Kronecker sequences possess a considerably higher value of linear complexity than those of the corresponding non-linear Geffe and majority logic type combination sequences. This implies they are highly non-linear codes due to the Kronecker product construction method. It is also observed that the Geffe type Boolean combiner resulted in better correlation and CDMA performance than with majority logic. The use of the purely linear exclusive-or combiner for considerable reduction of code synchronization time is not found recommendable although it results in good CDMA performance.

It is demonstrated with the Berlekamp-Massey shift-register synthesis algorithm that the linear complexity value of binary complementary sequences is at least 3/4 of the sequence length. For some sequence pairs the linear complexity value can be even 0.98 times the sequence length. In the light of these results strongly non-linear complementary sequences are considered suitable for information security applications employing the spread-spectrum (SS) technique.