Title :
Linear complexity of Kronecker sequences
Author :
Kärkkäinen, Kari H A
Author_Institution :
Dept. of Electr. Eng., Oulu Univ., Finland
Abstract :
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
Keywords :
code division multiple access; computational complexity; correlation methods; m-sequences; nonlinear codes; pseudonoise codes; spread spectrum communication; synchronisation; Barker codes; Berlekamp-Massey shift-register synthesis algorithm; DS-CDMA; Golay complementary codes; Gold sequences; Kasami sequences; PN sequence; component code combinations; component code families; component code lengths; component codes; correlation functions; direct-sequence code-division multiple-access; linear complexity; m-sequences; nonlinear Kronecker product method; nonlinear codes; spreading code; synchronizable Kronecker sequence sets; Delay; Gold; Matched filters; Mathematics; Multiaccess communication;
Conference_Titel :
Spread Spectrum Techniques and Applications, 1998. Proceedings., 1998 IEEE 5th International Symposium on
Conference_Location :
Sun City
Print_ISBN :
0-7803-4281-X
DOI :
10.1109/ISSSTA.1998.726194
