Linear complexity of Kronecker sequences

Author

Kärkkäinen, Kari H A

Author_Institution

Dept. of Electr. Eng., Oulu Univ., Finland

Volume

1

fYear

1998

fDate

2-4 Sep 1998

Firstpage

51

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/ISSSTA.1998.726194

Filename

726194