Linear equivalence of binary Golay complementary sequences

Abstract

The linear equivalence of the binary Golay complementary sequence pairs is studied from the viewpoint of feedback shift-register generators. Sequences that are synthesized by the concatenation and interleaving methods from the members of a basic code pair (the kernel) of lengths 2, 10 and 26 are considered. It is demonstrated that by the use of the Berlekamp-Massey shift-register synthesis algorithm the linear complexity value of 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 complementary sequences are considered suitable for information security applications employing the spread-spectrum (SS) technique in which strong non-linearity and good statistical properties are required for pseudonoise (PN) sequences.