Linear complexity of Kronecker sequences
K.H.A. Karkkainen · 2002
Conjectures for the linear complexity (LC) of some rapidly synchronizable Kronecker sequence sets of two and three component codes are given. The LC values for various combinations of component codes chosen from the families of Gold, Kasami (both the small and the large sets), Barker, Golay complementary and m-sequences, are calculated with the aid of Berlekamp-Massey (1969) shift-register synthesis algorithm. Numerical results for several component code combinations and lengths suggest that there exist quite simple rules for the LC, which depends on the LC values and lengths of component codes, i.e. on chosen component code families. It is seen, that for most of the combinations of component codes the LC value is a large part of the code length, which means that Kronecker sequences are highly nonlinear codes due to the nonlinear Kronecker product method for their construction.